{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 07 ``numpy.array`` 中的运算"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "给定一个数组，让数组中每一个数乘以2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 10\n",
    "L = [i for i in range(n)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = []\n",
    "for e in L:\n",
    "    A.append(2*e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 1000000\n",
    "L = [i for i in range(n)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 253 ms, sys: 30 ms, total: 283 ms\n",
      "Wall time: 303 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "A = []\n",
    "for e in L:\n",
    "    A.append(2*e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 93.6 ms, sys: 25.8 ms, total: 119 ms\n",
      "Wall time: 128 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "A = [2*e for e in L]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "L = np.arange(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 15.1 ms, sys: 8.97 ms, total: 24.1 ms\n",
      "Wall time: 24.8 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "A = np.array(2*e for e in L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.79 ms, sys: 4.36 ms, total: 8.14 ms\n",
      "Wall time: 8.03 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "A = 2 * L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 10\n",
    "L = np.arange(n)\n",
    "2 * L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NumPy’s UFuncs (Universal Functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5],\n",
       "       [ 6,  7,  8,  9, 10],\n",
       "       [11, 12, 13, 14, 15]])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.arange(1, 16).reshape((3, 5))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  3,  4,  5,  6],\n",
       "       [ 7,  8,  9, 10, 11],\n",
       "       [12, 13, 14, 15, 16]])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14]])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4,  6,  8, 10],\n",
       "       [12, 14, 16, 18, 20],\n",
       "       [22, 24, 26, 28, 30]])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5,  1. ,  1.5,  2. ,  2.5],\n",
       "       [ 3. ,  3.5,  4. ,  4.5,  5. ],\n",
       "       [ 5.5,  6. ,  6.5,  7. ,  7.5]])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 2, 2],\n",
       "       [3, 3, 4, 4, 5],\n",
       "       [5, 6, 6, 7, 7]])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X // 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   4,   9,  16,  25],\n",
       "       [ 36,  49,  64,  81, 100],\n",
       "       [121, 144, 169, 196, 225]])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 1, 0, 1],\n",
       "       [0, 1, 0, 1, 0],\n",
       "       [1, 0, 1, 0, 1]])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X % 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.5       ,  0.33333333,  0.25      ,  0.2       ],\n",
       "       [ 0.16666667,  0.14285714,  0.125     ,  0.11111111,  0.1       ],\n",
       "       [ 0.09090909,  0.08333333,  0.07692308,  0.07142857,  0.06666667]])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5],\n",
       "       [ 6,  7,  8,  9, 10],\n",
       "       [11, 12, 13, 14, 15]])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.84147098,  0.90929743,  0.14112001, -0.7568025 , -0.95892427],\n",
       "       [-0.2794155 ,  0.6569866 ,  0.98935825,  0.41211849, -0.54402111],\n",
       "       [-0.99999021, -0.53657292,  0.42016704,  0.99060736,  0.65028784]])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.54030231, -0.41614684, -0.9899925 , -0.65364362,  0.28366219],\n",
       "       [ 0.96017029,  0.75390225, -0.14550003, -0.91113026, -0.83907153],\n",
       "       [ 0.0044257 ,  0.84385396,  0.90744678,  0.13673722, -0.75968791]])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cos(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.55740772e+00,  -2.18503986e+00,  -1.42546543e-01,\n",
       "          1.15782128e+00,  -3.38051501e+00],\n",
       "       [ -2.91006191e-01,   8.71447983e-01,  -6.79971146e+00,\n",
       "         -4.52315659e-01,   6.48360827e-01],\n",
       "       [ -2.25950846e+02,  -6.35859929e-01,   4.63021133e-01,\n",
       "          7.24460662e+00,  -8.55993401e-01]])"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tan(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.78539816,  1.10714872,  1.24904577,  1.32581766,  1.37340077],\n",
       "       [ 1.40564765,  1.42889927,  1.44644133,  1.46013911,  1.47112767],\n",
       "       [ 1.48013644,  1.48765509,  1.49402444,  1.49948886,  1.50422816]])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arctan(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  2.71828183e+00,   7.38905610e+00,   2.00855369e+01,\n",
       "          5.45981500e+01,   1.48413159e+02],\n",
       "       [  4.03428793e+02,   1.09663316e+03,   2.98095799e+03,\n",
       "          8.10308393e+03,   2.20264658e+04],\n",
       "       [  5.98741417e+04,   1.62754791e+05,   4.42413392e+05,\n",
       "          1.20260428e+06,   3.26901737e+06]])"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  2.00000000e+00,   4.00000000e+00,   8.00000000e+00,\n",
       "          1.60000000e+01,   3.20000000e+01],\n",
       "       [  6.40000000e+01,   1.28000000e+02,   2.56000000e+02,\n",
       "          5.12000000e+02,   1.02400000e+03],\n",
       "       [  2.04800000e+03,   4.09600000e+03,   8.19200000e+03,\n",
       "          1.63840000e+04,   3.27680000e+04]])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp2(X)  #2**X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[       3,        9,       27,       81,      243],\n",
       "       [     729,     2187,     6561,    19683,    59049],\n",
       "       [  177147,   531441,  1594323,  4782969, 14348907]])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.power(3, X)  #3**X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.69314718,  1.09861229,  1.38629436,  1.60943791],\n",
       "       [ 1.79175947,  1.94591015,  2.07944154,  2.19722458,  2.30258509],\n",
       "       [ 2.39789527,  2.48490665,  2.56494936,  2.63905733,  2.7080502 ]])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  1.        ,  1.5849625 ,  2.        ,  2.32192809],\n",
       "       [ 2.5849625 ,  2.80735492,  3.        ,  3.169925  ,  3.32192809],\n",
       "       [ 3.45943162,  3.5849625 ,  3.70043972,  3.80735492,  3.9068906 ]])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log2(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.30103   ,  0.47712125,  0.60205999,  0.69897   ],\n",
       "       [ 0.77815125,  0.84509804,  0.90308999,  0.95424251,  1.        ],\n",
       "       [ 1.04139269,  1.07918125,  1.11394335,  1.14612804,  1.17609126]])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log10(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 矩阵运算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [2, 3]])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.arange(4).reshape(2, 2)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 10],\n",
       "       [10, 10]])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.full((2, 2), 10)\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 11],\n",
       "       [12, 13]])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A + B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-10,  -9],\n",
       "       [ -8,  -7]])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A - B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0, 10],\n",
       "       [20, 30]])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 10],\n",
       "       [50, 50]])"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 2],\n",
       "       [1, 3]])"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C = np.full((3, 3), 666)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (2,2) (3,3) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-145-cb7c4a36a7ba>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mA\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2,2) (3,3) "
     ]
    }
   ],
   "source": [
    "A + C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 向量和矩阵的运算"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 加法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v = np.array([1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3],\n",
       "       [3, 5]])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v + A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "``v + A`` 是可以的，但是在这个课程中，我们不研究其中的计算法则。有兴趣的同学可以查询资料自学``numpy.array``的broadcast"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "np.vstack:按垂直方向（行顺序）堆叠数组构成一个新的数组"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQAAAAE+CAYAAABiAs67AAAgAElEQVR4Aey9Z5Rd13UmuO+7L79671XOyDmQYAJJgCQIIpBUsuUw022vtmXZsiTLJIicE8Eou22t7umZPzN/50/PqDUWJZLIgciVAFQREiWNZLtXt2dmzbRky7JEUuQ369vn7PduvapCVSEw4Vatu84NJ71z9v72PvuELT+8eAJ4/59xpfcNDF65iD17t2HZsgfQ1tiMfCDIikBE0JDNIiUBUiJI8F0iCQmTkIT7npI00pLU7/oumYckS5AwCwnSEOGVRJppS4KO3a1I7A4x99mFkBb3TjL1KBW6UZQSOiSDLsmiReq1/EXrVyK/YQ7qdy6CNAikWSBZgeR8mPFhQSC8lxApSWla1v/6rwAi17puJO/R0l6rLH4bLc2tfDe5+iQzSa0jwxOnjkMCGXYdOX4Ex08ew9nzZyq0E6ZDTXPo6EFNc/rc6crvzCQClNNJpcN8QhBKiEAySEoKaQmRlABhIAhIhwlBri7r0nq6ZHvVSw4lKaMsrWis60Ah04CslJASxk1CgoS7Eq4e2sYp0ivbNQGRFDJSwqFvH8OJs8dw7PirWh/yQjrMIF3I4duvvYrjp0/h0JHDmi5MpdzvFsHJkycRBKP3HXlptKvSz9Z+/vfVtueI58nSx1sXzwLv/wpXes8oAPzlN17Cw2sfcsyVFkgokFaBdAuCNkEiEMfkbBg2nCSQkARCZf6EMngVILKQRHoYAISsYJ0g+BOBzBJI0ZfRKJCZApkqkA6BtAukU5AOEgjSOVefdkH9rnmO+Zs8o5PZWc+UvwgKSdeoBKxKQ062YSrxJ8cAH7/yxgOPyf3+RCpAkBQcPXHUMbgRsA8JAGwjMj3j2T1DAoC2n6VhX7Jf6yKhgkBGgSCMMn8YQHhZvzEN82cYCDKlPJLpLDJBGillajI7BQSFWAgJUo6OGJ9ChKEKElfH+lwbAnEAcebsURSF+fi2SwiSuQwkFY4KAKzT4cOHkc/nq/XzaUdjfuUfy9va4lYBwNDFK8B7wODFPrx5uR+7nt2MZb/5oHbeHeuXom1bC9JbE8jsqcPs7XOUEYviNANK85QklfkJAmyQggjypiVo5YmwVQ0gyR9WFrTtaIZM8Q1tzH+PYP4/L8BCLMZ8LILc4YGAaUqikr+0d4oDiEZBglpIMq1XMkiCeScSVZDSsqwhrzucHAPcMCLXaBts1+hVIfDr/j3jMXzt90n+ftYrISCjF0qFYdKfbaPAQCGSTYFgwd8T1QBUgzBiJwCQEVsEbRs7neaXJu1lEAShAxgyOa9UCAlDJElzXguc8kw7ujd3oHNdl9KctR21WmoNyvie+alVSN6lbdlURve2VizaMj+SLolsoqD1PXz0lQrzZ6gphAGCdEqvw0ePut/kNQCT/Ef9e6uDhR8BALjkAaAHb17uxUt/fQB3rV7iOo6qOZl0m0CmC4SMSkakVqCN7tVudhTfeeYnCBAcFMmC4QAwpb5NO6h1e5NjZCJ8t0DmCO7HYsi/EshXBPJlwbz37nTlspOySZX89XvbVDOQepbB4QW1gwT4rHVLCjIKTKKAYA19/eHEGUA72xDbQiPmCTPs8PKizM/76/8dtYw90efh9Rk5HKrmY8R+8vQJx9zWBpFQAcC3xWgAYFqBAmkouG/HXWjb0YrU9qIbKmYoZDIIKL2TQVXzI8MlUwiYdyCY+XQ7pM0PFRsF8/9ikdNkc4Ic4ygNEzSoqjO/nILNtJ0dkIWe3qcI7th0pwMUglbCDS/Onjmu5TSmh0v0RDLEkePHqgBAOmS9CDhhiGPH3LdoH37oAPCji8eA9/4JV/pO4srgRRx4fjfWrFqJNCURkbRF0LWzE9IVYX6+5xicF9V1qvEcl0ugYx0yvxufucaVRAa82GlFj7Tde9sdIxM8qGrNE6zBMshnBPK7Avk3gsW/XqIAwEZMhUUFoNbdHjhKZHR2QBbC4cC6BIL1Sa0LNRFeE9EAVI2kKlkZLhjBG2HbswtPnTqN6PX666/D0D2R4LBo+Jg3CBPgZZ1OIuF9JufHqiLI5ShZAqfRsN4ETWOSGg2glmDIdLzS6TS0fAIONbRCppIHn3WM7PPkc5gM9EqyzgbWle8BUqGrJ8e4rE+OwzDWO+PCMHRjZJbL95oH80oI3jj7BijJlZlr2uP4yRMal22i42RlElfW4SMHkU67316pLwVNWdC+ud31c5oaJuPknWZpgsgDQI6MXRDcsWO2G06SNhsFrdtbHICUBYEyf6CAUQsA8w7MgCwQyBI3BF384kInXPxvZL2O+aEKwUZBLxFA/HXihPt9ZHi2iYEi748fPz7qeL+2T1VwWl/UtF8tfVnbX3f44wtHgPd/hit9x3Fl6BwOPLcXjz+2CgWOd8icTYJZm2c6Jmdl6gQLNj6Madtn6Zi9Y1sZXes92lJDSJHxQqQlhSSZPXDMbwBQ4HNe0LnPAwC1DLvY8HcIHn1/BbLIQ1Y5uwABIBcUVMJP3dbikL1oAJBxyP4lQfC1hNaP5etwwBoxEhaLTo1LpUJkMimcOn4Cx48ew7EjRz0IGMOPDgBVCejsH9bwxogjOohtJmSKMxXpcOr0aZx845S+J0MRUE6/cRavvXoQp46fwtFDTo1MJTPD1H+nDQw3GjHv06dP49ChQyAY8ZmMd+rMKWXE06ddOSdOHgMZLBEy/imcO3cGfEfgO/z6QRw9fBi5NEEj0DLZJhfOntP6ME+CAOt19ux5vP76IVXBz5w+h1deeaUCgEbsNP4Nk+QRIp4oALCeLLeOdJgRdGzqdgInQwAg6NRBgmxVE+UQIBmipaHg6JbGYQoqqvUlwZQt3Q5Ayl76JyicchANqTn4IQDtXbMEHZubsfCF2U7AUZNgOgKnBDhx2Bn6tK1Vw6sCAA1+Gu/jAgBvXTwP/PodDPY4I+Czz+/Gw0887BqREr5T0L2j2zeAV3n4flMCIYcGbJwmQdtTzQ4k8pT+ZH5aa1Mq+U0DoKFlBABwSEEGJXiw06hp3C2qCSx+b4GCTDoZIktVrSSYv7HDaRtFNwRIhHVOnWMH5cgcCbUQD0PRCABQ8ml5Injtte9W7vmOTFRlcF+vypjcnkcPKwBgKr+FlK5e6nN8SAZIZTN6vX7IGb0ymYxaipVwvCZCQspms97YFSrD6bg38lsY/9Qpx+CUxIyvlncPAvqbDr+O48cdoPDZLkrab/6n/w1nz55VNdWYl3YVMjYlGC9K/iMHneEunUyBEs7iMi+qtSw3+o5Wfp0JYnkR5uf9ZAFAx+llQcO2bicoMuz3OqcBUAtRae6HpLwPBMm8IEGhQkNyu6BzU8mlpZaac9pQWnJIS8ExvhkBORwlaJCmSZekawoc5qUarqCYKeD8ydPIJgTphM0+VAHA+mOiGoD1x5hhTfvVtueY6SJ9fc04Q70Xgfd/jSu953QWwAHAcseM3vrfsatbGyChDV9S1E3tL0BmiFOP6gXd2+vdeL1IlCSiVi+1sJLxwgDZRM5pADTmdfqGZsPT1uAbWfNdK7ibNoGZgnRKkGX6sgcAjvcLHMulEYZZNb6Q4DhD4aYih6u/12oAahfstP7+fpVmDgCqjFILCIwbvUYMAYzxK2FQAQBKfQMD1ulvXvl2hSEpSclElDAEr4MHDzomlNBNfQUOBMb6LWTMc+fOqdSngY3xKIUp6XlvEjWanhoBn9kGJFhjYlPvqVlQ6hMAqB1wWMA4LCeXy6nkZzoCmOXDfuAUXyaXdsa9GgI+euK4q1uYqLQFtTGmjw4BKvXltwYCQGdlDB9S/efsUtIxoBr0DAiorZTTjn6nC6btanGaA5mY2kDGGQBpR8hJzgspGhTD6oyD0WFJ0LC1DJnrgCTIOM329CEHutqW7Gf+Rj8EMA3A2tJCxh1tCKB5XItZa9rvpgPAYP9pAP+Cgf4zuDLYi63b1uGRh5eiXMg6C2yXYNq++YqK6ZDqs5PEzfumOeOdl7xzdrW7MRef2TmSR0LyyEnKrSUgk6cFDfWdql00bZ/ikJXxCTTLBMv+fpnTAKgNPCGY8m4TZLagjpZgNlKjYOq2NkXmdE7QSGnPDiAgsHOpQSRoJfb1rIzrowxdvWfnnDnjGIQS1NC7lunH7STfgTpure2wRKA2AI55T5xy6iEZjnmSWGzs7rQPp2Ly2+uvvgZamDmuj16sc/RiXDJVqb6sRHjw0GuurTzTHzvmpDfj2bjayieD871+C4KKwYpaAIck2Wxey4oar8jwr732msZVbcCkoLcrkEAJdGb7UPtHpE2ieanNgvYib0cwWwrrk/JTegFpqSjo2t7h6CQrKNe3KiOnS87+QKt+hnakkMKiztFCq6BzW6uT5tRYSSOktVBAu4fNVimDUl3nVSeYtq7T0X051DTZLXk3XT1TEJYClJN1OHvQtVtYdP0YbUOzAdg7hiyPwH7otdeH9Z2WPRbzW5vZ99pne3+j4VDvWQC/wiXVAHrx4kt78dja5Y4wvLGvZftUN34is7UG2qgNm32HcO6+RdC4LusYmg3NBUJSh5TU6RhOra4eAHTc1Rqi7fnZToMg89Pq+oBg6c/ud419p0AeFzyAhaoBBLbYp1nQstupZMkCAcAzM1W1HUWofSBN20AZwjHdKAAQbXQynTEDO+o73/kOOO42CZjPU9WsAsaE7q2jLCTjeSMgF4lQWpp6aExfV1enqjS/kVioAbxxwoEFmYSMwYv3UebnPa3ONCiyDBrVdFwfGea8/vqrI36DDReovUR/v/0+2iR4r9OskWGGMSzrT+DUungAILgYwDDtwcMcTvnhD6Wjbw9jcv5W64taACDzc9in6ztoh6Iav73RAQDVeq77oEQ9dQTH/tO3dNpZASAhKObcULS4o9EJKGqpLYJFW2c6DbMlhVNHzuDId7+LDLUGldzeWF0UTN3a4dKRLusEHVu6nHbaJcg2cHFZgDNHzw5r0+jvoJRn3aKX2VlMg9J280AejTfsPkI/+r72uaaMYWkn8+2t81eAd4Dvn+vD1Uv92LjraTz4Ow4A5j9zD6Y9Nw1TX+5C95ZuTH1mujbm3P1z0fViB4ob67SR7t13L/KbkmjbXO8ameMjyaOgGgANSH6MRostjTpUxzYKZLE49YozCUTpeYKHfnYvpv9LE1bibsi9rvOS/M4x2XxB4Vk/Jqv30zn8sY2Cpp1NaN3Z5bQAafCLPIZ3BBvJFmNw3Mp7MhAlM8fnvH/lu2QYjum8WjiZxmRc66hoKILzFy9oGVwQwnqQUKhxmIQ+9cYJHD16GMeOHMapE9XpIgMA1k+BxKuapnKS6clsHFtr/b/zNzrmP3T4dc377NnTIAjQDkCjJ8umFGb5lFanz52tGCRZ90DBm1L8NE6dPqsGRgKF2RFMXWf+zMsY30K+yxXybkEM28BrQNYu9vujwGP3BAdV563Nc4J5fzYVU/e1YtrXWzD9+TYs2bHAqep5p0H1HjuB9nx09V9aNYCuTdNQt7eIjr0t6NrRhPnPz3BDzqTgzMEenDp93vUVJX/AlYVFBywZwYJ9s9G8sYSOp1qcHYEaqa8TZ0UOHj0J4cq+Yh0kybKrdqUoAJDRaTdhWkp/gnuU+RU4onQy2r21hX2z55sV/u2ZS1QA8INzPfj+QC/2vLwbiz91j/vBVJmIuByf854XG4MhjXVUze0dGZjPXl3PSxYFyep6AJUMNl1DAm4UTNk7E7I5ie6dM5zhhT+IjE6mXy2Qe5wRRhk/L5i1aT5KO6egZfsCZ2wsCZI27jP1jiChq7eKDmiu0UgmTStTUdmo3cADwDXSG0GMCK2jfMj8ybjRsT87nkTPcbSlJwDYvYUc3jCu1pVaRA3z67Ovo2kZTGszHWz3urrhc9WWN0NKcjKrvmPeVFfTjpkMCPiOEjrPIaGfsjPbQTaXHhUAND/OTpxzkrICXIFbEWf2CotnGhEBgAB49HBkRSCHdhQYvDjdS/rju7Sblz99+AiKfkFRoH2fhDQmnSBgfEpy0ibTZwW5bBl5acbB46fdysHQzQAoAHA1INuTdMR0DLO0LbnfTmCm1vbdg0eQKjZDAradG4ZQI+KQrhYAyPScYTEguCEAuB56HC/Nfz1zDHj7n/D9iyfx5pWL2L53Cx5avcKhI5mWjUo1jI1ee/F9MglJu+k3/a7LcLkkmOv+eaWcqke1TZcWuwUbam3lHC2HGWlOHfK9b3iCi3U0y+dlQNNA5HVTQzqfyzyjUz4Bx9FEbDdNR3WazwyjlxGfxauElPxMW6MBWNpquqpUGPauBgCUkZiXvVdpUV0XwLRHDh7C4YOv4Y2Tw9VHXeNeWUNOBh25zqBSdiV/Vy+TyMxD8/EqOtVRXpV0vp3099IAyZWV9k7D6u/8zrf/D9VSTnKaj8PB0Yirph4ax9p0WL7V/iGTMJ61sYU6k8C+J42QVihcSHMiOHe2D+dP9eh6D+1vai80CnKFIGmCQoGMT4Me05JGQsHxQ/24cPL7TmrTqClcVpzTS6cCbUmwpZESRDVKZ6hk2aEkkJWyXjrVre9cu1r78jfYfTS8bgDwbW1tY6G272j9MNF3f3f+CPDuzzDYexyDg+ewc882rFy5Egnd+MPltSkkJBwxHx3SAi95hNpAbCSOo0hYHP8bgSecldUalR2TIOKywQtI6pXT9QIECls7kJScGvI4VaOESWCoXEVIkpdfH848k47IK3P/JEJPbK4jRiGuSgM5QrT4jhFuHgBU8q0wBtsoyoCubkpYWu8qY7Hu1Q726SwfCy1OzfOkAUDrxDKGtwelM8fr0bowb04jjgoCVg9qFLyvya/22fWPaw/eRy8yGjfs0Jis+06SSaSCOiSENEPp65iyUjeCAGmQmiGBQ+nN6pBEQrLISD1SQQlhJgvhJiQOAXQtgAMCagJOG+AaFmpoLe7S9SyOzrjILSdlvQgAUQa3e/td9mzhRw4ABvvOg0YAMwLu2rcFK9YsqzAcV9RxaW1CGZuqEDskjayioCde7WhPoKaW0+inl1ugoQ2t1la/aSNRndvWxuH8LVVQ3enlQIE7v9iZlPRpTvGZNGMnGwAwpMXYJLZfjabSQ+s1nKiMwKqMNZzgq/kMtwGMTBdlzsi9MYCFxgCVZ99OnnHr8vmK4U9nNIyhPTNU6+nTWT4WWvya55sFACyf9hL+ftYvl8/A7ABcU1GZrqutR6U+Ne1r7eFDa9fakFLdAQCFDJmetMdhGi8uAMoiyLqpwIp2xTK9psN1KNygllB6yiArgQ5HnXbo+4u0Q61WZ49SKpR0SbAye8otEw4zfsWgn3LkalcKOwonXUfAdCxruAYw1vNHDgD6BvoBvI++vh4MXunX7cAKAETPlFtSy2mW4QCQVMure+8a3RGqR1+z+DOPNJk1wqAECLuoRtJIZOqpqu8OianKGZqHlDh+azLLHGZU1HGxR3EuFuJYWcfL3iBXI1WM0KqMVUOgFSD5YACA9XAr8KpTX1Y31tXundZQtaZXiN7iVBjOpRnWpn67LN8ZYVbztd9vwGTPLiTzW1wDKIIA8xrB/KyL1cPCGoYfTQOwPomGBgChcDEUQcAAgFLfq+OkM9KSlcXQ/8asTj9nQW2S28K5QY2zUSwjSca3unJ4QRBIkIlzbldglAZMkFEQ+bxVSJDWuMQ9+JgDwMClPvDvUn8vhq5cxt49O/DYqkcqSMqOoBbgiNERBe/5TtHUGj9KiMrYHhh4b3HGCzUPlmHDCN67zmKZjiisLlHmGKMMq9Ow0P2GKiHW5FMh2Nr3t8uztc+H83vZz8MvTotSkrNeBCkfRmlpWP+6ejM+NQgnuNziKtIP867QI2nThBHzs76P5m33I8qwdrLww2kv44/rDi8P1ADA7l1Y/dij2lA0Hg3vjJHPky7YGnSs0DphjLC2PpMuf0S+tR33Me/QEYRa+/vGe/5wf/+N9+94v+9mf/9w22vy9F/z+2sBYN8etxuQzE+Vr7ZDap8nXYGxGN/ej2BQa2AX3nD5I/KvaZDK99r3H8yz/b5Jt+sNM779Pmtve/5gww//93+wv/fD62f/O2MAqO3w250BbvffX0sPn/DnDx0ARkguI8DRQ5MQFk4eQWvz/YR38Ij2jX/v5GnmE9xmMQB8gjs3Zv6KETlm+jHofDwAuOkNZ2N9C0cQaa2EHv5skt/Cm16/EfUZo+HieDFzfRJoIAaAmMFjEL2NaWAsABix0MMkdm04AgVNYl9vo1p6F7pjsIafjBt9FxPv9bZznC6mHYHEABAzQswItzENjAsAUYk/kVV948yjjz92v0UagP2OERrLbdz5cVvEdowJA4At7zVGGi2sML8x8Ujm+tAAICb2mNhjGhhJAzcMACOYnuv4o2v5PRgQMCLrvE3tNECohmOP96Njf7uvrN8eUY+R4GNlxmHcNjENeBq4+QBg0r8mjABAZVNGBBDGBgBuBHGbQapMz8rX5D/iOSbymMhjGhiXBgwA+gcuYnDwMtxegFXV7Z6m6o81BBjBeNdmzNodfVXGt30HUQ2Afgd58Eh6GAjojxrnwAnLd9wGiNXCkWph3Ca3T5sM9feAzgEv9V/U7cD79uzFmlWrdN+4bQbS7ZNRoiAoqEGw6iG4IpENKFRqjxwOEAA0Lfdg25FgoSBBj0JMS0Dhfm2ex8bv6oHYn/HGdzwazM4bsLK0Ln6bp39HAHDbQWMpEINgTANj0sBbveeA99/FYK8DgA0bNuBTn/oM8qkCyv4kGCYuep9tysDKxJGDN5RxPbP7/dWU2ik9tolnzEVtAu5ct5nPzEBpXQ6z6fWVZ72RuenGmT7zeB4gj3PmIaH+kNH5W+Ygt1lQ2pNy7wkELJdgwYvlMuSZcWlqEzxOyvaR33oC4MGZdry1HqGVSOhJOmM2fBRQ4/vbR+J+1Pr6Bxd7gPfew1BPL65eHsSBFw7gid/8tOsQPSnFn6jaJQjaq663VSuw47d0GOCZ3E5QUeYz5nffyJTKEDyF5UvO758e3EgmZ1lsHLplWiD4zD+tdQ4aeagjvxEUZgvkJQ8OfKYmYgBAMCAI+LPgCFRpPRDi1jN/lMn1FCNqHzz+7KPW2XF94j6ppYGrF7+n7sGvXriC718axNbdW/DQ51eqdL1z/XJ07mhDZlsC2X0FzKHH1aygyHPiKicFkak985sE5hlr/rDOigrvpbFqEPWC9j3NkGnueHFzE62nv/Ik17sEM3/Rqc5C9PhxVpoaAl1E7S44DYCnvvJI5gTdj/P0F39KUUKQUhdhBABnV/ggGJHSn8dCm0uvD6LMuIwPFtw/ke19tedNBYChi5dUA3jhL5/HnSvvdeNsnqtOnwC7vb90Sl0yoqnbZHJKZ3/ksr7nuzEBIImmXFmldGlzwUl7r+Ir81PlXyC44+d3YyqaIA97/wM8CJLnrxUEXVva3HHPrIcOMXi6q7cXFN05dTz/jQA1FgCYlL5ZHWqqP/MzD703K+84n5jJbykN/PjiGeC9t8HTgQeHBrB//36sWrEGdWHRMXKroGVLoztfnUxHKU8VnpKaAEHHIQQBU+H5XQ9r5AGWPCrcPAQ7Z6E8TZgMS48t0u0ZlyBAXwB3CT6N31O/gJ3vFyHLnXdiMnpaGrXsGeunueFAHaU7XUTnXF2eCZHamFTDIZl/OABEZyZIUPTQ4lT0yYIB45snm2jHFItFfU/HEXT1xW906FEb18qLOgWx+BZ3tOED09l7C6Plx/cxUFwXDfzkwhvA+7/EYN9ZDwAHsPqRx9EQlJ1kbRZMeabTSX2OuesECzYux7TtM9SPX/vuMqavb3fWeQIDmZ9Hfqt3YJ6a6qU3/QEEoR4nznF65542BwBMw3H+vYIl79wHedC5B1+M+U4DoAdhA4CUQAGAwGMAwJNcaTf4siD1lHPwyLE/pX/tYaZk/LoCfRjwqOu8+r6jg0x6quFlDDheQ5Kx+/r6QDdXdK9NV1tkUL7nEIDpORw4f/48GhropswRJxmX5Vy4cEFDvicQ0KsM82Fa5y7MuQajZsF8ebEMeuU1zzPMi+8t7ziMAeC6aOAHFwfcEICzAIMD2PvsXixfvRJSl3KStkvQtqnZMbYezeyl/yaB7BA3ju8UdD3V5LQAMjQdLdjRyqYFqAMGAkBShwAKAJT6BJU5AlkruPOdxW7IMVcw+2d3QR61IYAf65cFXTvaKm6b6FwklS67uhFECvQrwPPfk5VTizkdWJmipFEwkdSLYPTtb39HGciYN+q5dqzGJOOR8Wnptzivvvpqxc0XmbSnp0fBhICi/u68QdAcajIdy2Rc3hMEzFOvSXc+mx/DaL2oLTBdtHyrRxzGIDBpGrjaO0C3AG4acLAPew/sxvI1D0NKgVOtpwiatjQr06qHFqrd9BfwbM5Z5TkE6BB07io6MOAwQQGAIODUfgUDPyxI03AXCrp3dTljHq32rYIH3lnmfALSF/tiwdz37oGs8QDDYQXH+Y2C1l1tTuLTN6BkkE7lkcwk1XkI1xHkhCDDxUNRA+DwIQBBwIYAbDAyNJnqm9/8ZoWpx2tIqvqU2FT9eTE+Gb7qYtwRo2kH0fwICpTk1CLsPUGEzM+LmgTrZLYF1o3xqVVQg2DZBJBYA4gZ3ujnusOhgTMAfolLAxwC9GHT5qfx0LJ70dJQdGP9NkHbtqnKfKUC1dmkqt9tB2ZApnofbHWCeXvbnfQmAAScFaDrprzzosIpOjJwUtCYa1EA6djUqap/SADwlv8HsQrL/+UJ3PXOQ2hAGbPfmeq8B9P4SEneJGihM1GCTskv9CGwUPrT8Mg1AAlRr8T0ChOV/NV75/baXF+bys78yVwMjRGvxWBkdjIoGZMAYMxK5iQDMx+GZPbo0CIqzcnQVoap9vo7RUBAoAbAPKgNMLS4Fqf22d7HYQwME6aBq/0EgLdxuf88hgb78PwLu7Fi9f3O2EfDXrOgfddUx3T0sEqvqW2C0sYWdz/TxWlen3aMzAU6AZfz1nmPLs69lwIAmZVeXRoEU1iERKsAACAASURBVPdPczYAvvNagNwpkFUC+bwgAzcsoEtwnXlgnHpB464ZldkDnVIkMDQKOrYXMH1bkwJNXkrqvqzK9FUNIAzT4EUAeOWV7w5brEMLPj3hUCUnMFBlH60hDSiM6Y2pCRwc95NxjemNeZkvmdzSMG50xqAWACj1GYflE0TI7HxmSJAZrV7xu5jxJ00DP7hwGfg18NaFXnz/ch/W7/gq7v+t+1WSzl23BC07m9Gwu4jGpxowa/NMNfYtemEBClszqNuYVm1g6YF7Udwaon1r2XllDQR5yYMuwulfQGcOyOhU5cmwlNjrBDLPzx5wTp9TgLzmCVbiPrShDivwoHtH0OFMwWxB/bOtDmgK1AAo5V1+zTsa0L6zQ7WAUOqdpqIrFKvMT0Ao1pU1TS5XUCAgk5Ohe3t7Ve0mU5LR+I5qeG2DcuxNyU2GZZzXXnutMh4nEJiaznRkfuZPm4DlwzhkaH5j/gz5jfmZAdAAhu9ZF4KJpWEcagPRWQTLOw5jAJg0Dfzd2QH6BsUPz1/EW5d7sOvFbVj4xB3O6k91nkzJ6ToyKS3yVNcZ0hLP72RMqujeMu+s81TD0yhKWq3xPF5Mmd8AoCSYtmsG8ptKWLp3jTJAXanRqfDMi3YAzgYs8HmnBPPWzUXL5mZM3zrbqfs67ZiA+p5n3VgXXroMmNNw3pW2rj4cDgIc/1MLYGOZoY33JnHJYCbBrUEpeXnxvUlxxrM0Fi8aWjx7RwNe1NeeSXV+JwAwP4trIfO397yvzdPixWHM/NdFA/9w7ijw7j/irZ4TuDp4Aftf2o2H1zzirPP5hLMDkMm5MYchrfxkPhtzp5KQdKL6Peks8TTGFfyVpk83Mj8vLuhJplwezC8beDfNDH05BjKU/PkQkvLxrewsfcDT67BPw7E/v+UE6kiUzEwvrupgtOqF2Bn+bA2AAwVjbAvZiLwfrTHHej9a3Mm8o8TnRe0gWkb0frT8xvs+Wpr4XQwUw2jg7y8cBt77KYb6j2Fo6BwOvLgXj616FIEICiH9qVOKJ9WFNZnKttlyow19t4fCefU6Z/kPHdOpB1pdjhsgp15aOSNgAEDXygUEUkSovtgLCOlu2VYXMh63+pK5yfipnAKGemblcCIoQhJlByIcVvihBT0Gc+6fIUGAzDEWAERtAy6ek+4fFkNRso+mSXxY9RlGIBxixdcntw2G+s95I+BpDA1dwIEXd2DF2geUYcOcc6nMpbVJWva5qCfI6N78ggQo8L2XmEqsyrieKcmYoZPEzle7d7etUttL/WQIagd028wpvMC7YFZNgRoGLwUCb+HPBZBcDpLLO22CgGCAoW7C6Z7caxsMefn3BgZR5uf9hw0AnEEwRicI2D2ZLnofM2EMRLeEBi4PuPMA+ge4FJizAHuxYs0ylaxhnsY8QZ0BANX3kAtgkjrfrgDgfc9X/M6bJPfTfmRAEnIFBMjQSQcsTSLoEEEzV+YxXUSiExSYP6U5Fwsxfy7yIeCkvZR3e/6dpHeM7zUHlkFAiYDDRxUAoozO8X2U6aP3t6TzY8n+yZXsE+3bt3ovAHgXBIDLQ5ex/pmteHTFamcDEEFrnbe0M8NMCMk46R1KDmnJKVPS0s9hAi8SKqfnMpS8TFMBAGcb4OIgMu6mqbOxvVyP388LHswEyCZykIxbpltMC35HBP+dCMq6oCeBry54DNu678PGlum4RwQl5q3A4MqrDDHUzuD2AhBECBymBYwWmrGPYdT6rr/DT8PdiOHN0kZV/FpJz7KiMw5kfFr5YwCIpb7y0ESZ+Xrifa/PDQH6Lp3HpaE38ey+v8ITKz6rm2nIfDNFQEnN8bVWRgGAWkARgY7l3bLfRIJz6zy6K4G8pFEvoV+O66QxQYISOVtqQoMI9te14xkRrBJBlzJzDpLi+F4wTwQ/fHwlNtk3CbEy2YnfkjReqmvHEyKoZxo/q6DLfSntqUWoGh0i54cW4wEALexkNJvLN8bnezJvlHGvlyE5dWhAwFkHu2cZBB5+Z0gQYHm8DJhuOQFYv8bh7akN9F85h/fxNi5cOY/+Nwfx4vP/Hp958NOYIoJHRPCn5SI2zZimQNBAO0DIpcD1kCTH4VlIKg9J5yEpbsvlfQlpKWCGFDFfiijQbmAzAFTxy2UdVmwsNisjt5Hw+L6YgaQCLBPBH4ngl/cvxQERzOB3P2XHcwi2t3RgNYcMHP9zNkIlPuvF/QJcfcjVimW3GcmGABFbwAgtwBM+59k5TUdmJKPb1Bvn3Y0pr4cZmZYMz3yZnkATXWTE73zPOKwD7435o1OU11N2nCbWIMalgQtD5/Au3sb5QQcAO7e/iCfueAz3iuArzV34DRF8WgT/pqML9wRZNEpWF/lQveaVkaRe6YQbm7NAbsV9RIr4g/r5mCqB2hCUUbmazxsO1ze3K8BwTC+c1ksJGkXwRRH8ZOndeHfOPHxdBNP4vUCAcar+us4OrDQAoJEwRQYKNW0TZyukCcKLm5EIDqoVXGMYIKILcIwRjfG5oo+LdKKawbiN6cFkrHi214AAw4s7ABmXZduW4NphyFh5xe9j5r4pNHBx8ALew7voucwhwCCeffYb+I17nsCfd96pDNouOT0B6DERbGhpw3IRBYcl4lT1O0RwlwgWe2k9VwQPSBqfE8HmZAs+KyGWSl6HA2rVD7lZR7ChvQuPRhhmZZBQ5r/82Cr8tQh+2t2Ob9gQgFb/dEKNgs90deqwQTUHMngQqkbxfOdMfL1zNpp1SrFQ1TpMC7BZgtqwBgBqG5UagDFs7beJPpPBqQGQuQ1omJZ51+ZhAEAgsnKvFdamj59jYJgUDQxcckbAS/3nMTg4iL3PfQOfu+cJPNPmACAnbuns4yLY2VjGUhF8bc58fKW7QSUxx+t/Mn8Wvjg1p+AwRwS/3z4HOwstOJBpwYbCbHxh2j1qvdc1/4mkGwJ0TcEKDwDUJP5MBG8tfRBPi+ApEby/7G7sEUEn42Q4vEio4W9DV6cOHThEUSu/ny3Y3tQOgkCTLjpyww5OK46YJrxOAIgy7mQa2NR5S8N8qFWMxvyMQwAgw8cAEDOy0cwtDX/Qc0FPBb7ac16PBNv5/Dfw5FICwF3K4A0SIiMCAsC69gZlSErf9R31OhanNZ4Gwi9OKysAcOquVUQ1gH3NM9SgR4Md1XtnSAwVDNZ3dKmGwR/XIoJviuDt1Y+q1Z9j/f/nkTtVA+A3KWQhuYRqIlvbOzVvAkBl2tCDAKcsdbdimPLThn4uvZbpo88T1ACuBwBqGdk6kqDAJcHRnYj2LQaAmPGNFj6Q8CfnLwDvvIsfnT+PtwYGsePFv8Dj96/GptY7sdbPABAAeP+VbhrX3BTc0/UFZUStZEbwrzvyqppbpTlO3zt1hqr+qRxPCBI0cKovnddTgbZMn4s1BIWEA4C3Vy3D/+zLoxaBVQ/jfxRBO5mah5MU3JqEjW3tapPQ91TvdV1BZA09/QjwRCKu9xe/sCbK8LX3kwQAMrX9xomEZlOIxjWV3jYCRb/FABADQJQebvm9AcDfnr2IHw5cxpYX9+Oxe+/H5tJ8/K6kdNzNSnC67g+44YcbaBKCTVO6VSvQCoaCP5zehIcoiQNnBPyUCLZ2cluugCsKGa+YbISERWQkgWe65uGzKrHdgp+tIvjbOXPwD2tW4b8svgtonYN/XrAMUxUAErqDkCDylc42rYuq+pxhkCJyklY7BIcnXLQkSb9XgAbCa80AEAz88V21jE3G5UUpbQxLLYDvJrMTj9Z9S2cS32YEuK2XeZm1n3lzN6G2qW8bK3usMBo3vo/BY9I08KOLF4B33wUB4EcDAzjw717GI8vvw6OSwaZZ9yhDkam+tLAFNPyxAC70WT9njo7h3UIdwfp5XfgUJbKPw1mEL3TkMd1rDNwZqId45ppUK3iqoUvH8hxCcJ3BkyK6LoBS/zA1gLoZ+I9mAyi4nXu0Bzzd3KiaQxtPFuIeBGlESZJ4pqMVGzobdPjhNglFNgzVSv3os6+vMafVnyFVdb43hiWD8j2n68Yaw0fT897m/HnPrcPR79QAbHcg4xnz894AaSzGt/fR/OL7Kv3FbTHBtrja52wA3A78w4EBbH9hNx753GNKqBx/f2XGNGxcsEA1AV2uSw0gEND6/4ViAU9N6ca6rjZsaUrjT1pLaKTBLpnT9LQFfKG9Dl+Z3u5tAHWQfIOO5Z9vn6LGPq414HiehkACAVf//Z93r8I/d87G/7vycbUJcM3+/ZyKFMHz2YJqDtMli0A3ItWjJAmsb+vE1rY2XVSkzKN7CIbvBxixBsBrAGRCO2TDmJzMaXv0+Y3MaZKaU4TjAYAxKPMz+wFDHvRBNd+YnYRKhjewiRIu41s+Y4XR+PH9BIneg37cXgJRAMC7uNpzEd+/PIC9L+7F/U8+AmkKUSqIGvYeINOz0TiPz/l+L5k5A0C1f5GITulxKpCrAPU4sHQG5aRb2MPpPo7ZeYYfG53p9y5ejI31ZXxhzhR0es0hTAZ4UHL4bU4Teo2A9gem+WL3NGwuN2FLqUmNh10SIqGHlOYVAB4UUY2E+wr0EBKq/gSBCQwBjBB4eIep6/bOmNeeLfzWt76l9bLn8ULTBBjyqs2XoMA8DAzsfizGt/fjlRt/j0HhmjTwI+8a7HLfRT0W/IUXn8XKxx7WBTQcv1PFp5pOSRYkBenQbbnV03y9qy/G4xHcvFxhzlMP5/s5fOBljKwLc/TEIOdhiGlCnc93aRmPZVL70OW+Pk8uGGI+nE3gNwKSLgH2QxJ+4zs9JoyAoguAGF5jEZDfp0BmijaS/taad/ady3VtxZ4NDezbZMKxGNjeTzScTJlxXKPPOKzQwo8vON+AUQBYtfJhN2/PuXYyp15JJEIHAMqw3O1HdT+bqqzkU6bzjEnmV0DQ8bZb7qqFGnOq9T7l9vVz1Z6Bhx0hxvy5RNje857vmJ5x/HsDAX1fmfe3+X+GEwOA0RjOyoiGlNw2FGCa6LfJ3I9W3vW8m0yZcdwq3cRt4dvirR4HABwCXL0ygAMvPYuHVjsNgI3Effp6BW6zjy6+ISAoQyYdA3OLMM//54GfnjFVEpNRjXGZxpiX701CEwgCqvMBUnrgiFvaK1zRJ27NgC4XZlrLo5b5DSQ8+BAU7GJ9tc5Mr9dwQLgW09lvsdDi2jM1BV72PJnQ8rrRcDJlxnFjABhBA1f73HkAZgPY//Kzzi8AmY1jUm71Daj2p5EIsm6NPdVqMjDjKONzbM+LTOukokpmY9rK2QCRDjCGZD7K6FxwRIbndmHm4/JM+V2FWnECR0T6j/gxfghA8KlcfheiY/6RGsG1GHC0/PmOBjsb048VZ7z31yp3Mt/GKyf+HqG5iKCI28W3y+WBPvDvcl8vhq5cxnMvPocVj61w0pKMxD33ZKJaRxQVZnRn69FSz63A7qqOz6uMV6MBML2BgE8XVtLX5jnxTjTJb2Hc0RNvu7itbsO2GrjkAKC/vxeDg5fxwgvPYeXKFZV19qZCW2iMNVZIJh6NkWuP4qo+34aNHkui6xo2xQB1C3glBoBb0Kgxg8cM/nGhgRgAYgCIJettTAMxANzGnf9xkVJxPW+dRhUDQAwAsQZwG9PAjQJAlHicYdBmAsyS7xvXZg1qwxjdbx26x20bt+14NHAzAYBgYFOBI6z8tYxvz+NVMP4eE3FMA7eOBiYLAFGJP/r9BCV/DAC3rlNjhonbdqI0EAPAbTz+myiRxPE+uYBywwBgktxCc8dtz7WhEZO9t+c4/OQSWdy3H92+jQEg1gBGH8rF7XJbtMstBwBb78+QUt+kQawBVNvC2iQO4zb5oGngwwAAThcqEEQBwd7VhPTtV4kf/cZ9/jGIfCIYhhvNKoIh2scf4/uPzW+qAMCAPxFonM1AIzrKmNBCk/i1z14DsE1EEwEAxnVuxbm2IKI98F5P+onsMKz5Pqycmm8jfkP8/UNhQGMSPa/B+oB0Y3Ykf+LUtfsrMVyzrKStoRfL/3pDo+cJprffdu263+Q6TrBuw+p0ZSDiGWioD3ok2MoV7lw9bgdO+EtdcUek8YiO8tN/BgDqKpzuwnlOf5VRlZF5BkCdQEp0+lE9a9CtIUgjlCxCSSOlfgfTroPpCLTsL55NyKPG7VARDy6qEfBdwq1HcLsSPwKNfD0dcxuk4TZz0gPPm6hoc/TrUKGdEEkeuML+ZZ/7E6HsrAfSi9JXNL2m9aBg72va0tGZp037ZnGNljQf5+3alePrGKHlYUNay8eH13tQzDDmrMnzlnx7q+8NAL/A5f6zGBzqw/YdG/HEk6uRT6dQlw4qR4OVsil17sHGVybWjmEjJpGQpDJtggeC+gZKSR5pPbY7CVFnHREbQE4wY/00lNYVMHfDjMpho3VhA7LSgpy0oU4aUCdF5DUPweLtC1HcnkPD3hKkUyCNniDssBEeTsLTh7LufSgppCVTcQ5CRP7YoPIH0fG3qAw77JQhT1WuJVq6RTtx8hjOXziNZOBOg+YZkIx3+MQRvHroMI6fcE5Tqf0pOBDsix70k87vRFaSKiAqAkaFAQFBEGbSSgthRpAjPfBdSpDJ2mE1PIGKJ1e7Q2qVZpmeNKT0FCCVopPZErJBEflUQQ+6OXrqBA6dPY1XTx1R4RMyja87T5Hmwa52XmQUAHgCdPTZ0nwkwh/0ngHwSwz2ncXQYB++/lcHsJbHghMR2Xj8kW0C6RYkOgSJwJ/1p4jp0JoSmwyvAMBGDHkij3unaG4AYERH6f9lgcwUyBTPzPUCafZltQukw5g8dJK/RSDzBYmvC2SWQPhMhufFMgk8DD0AkHiyQhdhw4/WZqPzRJ9isVjpvI9ER1jbfMxDA1ljhNq2NW/L6UyiAgAl0pIIDp48AknnECSyyAV0+EJNUCCkjZJg7sYu1fx4qrS+N+2S/U46CJMIMvQV4dNQY6SGSZpoFwQNTgjx+LnKCVbG+KQfxiMNUrhQO+Uz6+Yd24R65H0Cbwxc0BOz61KCdGq4/cJ+twGh/X4eJmtnSdq7j0R4tfcy8D4w1NOLq1f6sOf5rVj2+fuVmRatuwtdu1qR3R4it7+IuTvnaKPQdx8P/WRHpFRVzyvDKxqzI4iibFg2KpnfLh4yys5pELTubYRM9w0+RyCLBIt/sQh3YSEWYTbmYDZW//zTCjx6zBg7pVXQuC/pQINEEeQgiYxePEqM9eH5hXQ3xvrxohHRpL8RJ4/zYoe8+uqrMQjcIsAZi+ANALK5tDsNmjTk6eXgqeOQMESYoPaYQ0FKKEjBaYhdgvyWpAMDMjyHBB7snSBIQMI0Ah4nVye4c2snGjcLuve2o/GpJizZPhvCYSTT2W8mfZK5c16r5X29oLyrBZ27p2Dm/jlo295d1TZ5FH0hi1PnTupJ2Tz0ludVktkp4elfohYAjObsfaVsq8OHHV7tHXAA0HsRVwd78G//hxew+NEFrqHIZFMFskccsxoyGmqS2dmgDG3cZmjMcAQAJNCYLzoQ2ZJTVNZxfatAHhXo/1cE8jWBfFUgn3LlBkEdgkyoHdG9o85pJCWCCdW0IiQdOsQuuiPG6aCUjkYUACLHmVlnsBMIAqN5A7qRDormb/mQMD6y6t9NJL7ob7+WyhsdFiS89AxyPFxWQAAIslnkSw06tg9TGcfklMobBLLOCQ+lNzKrMbSX/hKkkaWviKygcXMAuUcgFC4LBEK3dqRbpVUPAib1zQ7VKJi6fwpkiU+3UFDa2ey0iII7F5N+J8+fcUMUHkVPAGD/8vfzmHhjdGqZpAELxxoSGZ18aOGPe44C+EcM9p/A4JsXsP/AdqxZtQJZTs2wkTsF7dtbnWpEQCBaczxGprWLIEAGFdoJUnpwaKjjb0rnFCTkFep7SmmCRtu+JkiXz4sq/3KyfwbyRwL5Q4H8rriOoOomRWTJ6FnBjI1NrjPriNrNELovJ4E8k0FqQ1brRuYfDwDY4Oaai51kHTVeR3CcF71ef/31Sqezk0kI0YvveFm+Vk7Uv6CphhbPQktzrdDKIqAZITJ+NH/GqQUh1uNa5dR+q6ur0zayvKI+EaxcfmPZUSavrbt5RArCBCTlXL6F+TwkkcChk8fVDTwFR7Kl6BivKOjY3awCqGNTtzMeUy0nI5MWeVHYBLRFpVEK8kofDfuyqlXKHW74qkNKBbwQqcgBtupEhvRcJ5i2udtplzMEMs8LvW4HNLQnZOgTQ3I4c+SiDi/rUhm1h/G3WD+YhsP+4LtoO47nTaq2rT6Q55/0HAbwUwwOHMPgm+ew/9mdePyxlSjyiG82brtg+qapeq8+AsqCxVsexoxdsxVdO3fUY9a6bj/WckxO5mdD8RI68KwAQKBqOhm5Y2+LU+8JMuyApYLZWII579yJmT+di4ewFHKftwlIAVkyugJAWwQA6p0GQBvFnwpSf57RjsxKpjJEiR5oagRqDUsAIEGePXtWr9rvFm+ioRFBbcj0LMMYgx6IWDbfU23kPd8RTFgfkyIkoomUzfR0X8b0jE+GtDyZL99ZviRIvqN7M2NG+ixk2iixsg6sc7QuBD6+Y1n8jXx+5ZVXKj4PDRSYvzFAbf2tzCBMIpHMquaYyZY0PHLipNMoKVAosdsEU/e1Oy20W7Bg53ylAR3/mzT3miZnjLKSRmOqQTXFpu0NkF2C3PYSpm2b52xGpDM1/pV9GCJNewDH+82Cll31KvAW7JuNjpe70byjW9MFrWkkMoLGfBoZyeHsa70KIoUw72e5qqD/sQOAH/ScA95/G0N9pzE02IO9B3bi4SceduoVVf5pgs5t7drwCaIrUZSSf0sCsrtqyFMQ4JgsR4lN63tGQ6cBhM5NV4IAkNC8KgBAQw0NfncIPvfzz7vOJmo/LngAi7V85wI8pcbAzm2drjOZjvaHdBmSTKpdgSphWqgG5rRjdXw2xhCAv8OYkNKSF8ettQQ7medaxucz05vUJ3GQAcj0UX+EvDfpYJKaz1EpPlY9LB0ZjvkYg1k+/E1k1Gh61ovMSvdmbAOrp8UxIuYz87R2YZ5W3mhxDbCYp/1mi2dhtX5pHevzCPhiqqTHwR8/ecrVszFQGmF/Ln1hiVPjZwjm7OtUgFA3dWR8L/0JCEVJoKR9T1AR3LfjIactUDioFjvLgUqBqnmTE0ychuRsFmmpQdC5vRGL9sx3Y36CRaege9NCJ9z87EOd5ND7ag9KkkejlHWdSrTfDeT5+/k+Cqq1bWdt8qGG5hdgsO+8zgJUAIDjIqrWMwRtO9qVsZOckkuUtBMyz9VB5noJ3SqYsqPBSXQ2HKV+4ACA03FKYB6p07QVpAQdezrcEIDWfA4B7hXISp8fO+QJQeevS26mwNS9RkHbdg8AdTRAJpBO5ZFMZxHQa1GCqn8GOSn4BURVZLZOYmNrfTwAWAcxpDQbrzOi6j/vxxsCkMCMGWoZI1red77zHSVGxmf9KGUt3Xh14nfWhY5HKX1NEjMvSnrmZ78z+vtNuisTROwBVi7zIkETACw945KJyewGoFaetasxwWj1jgKA+pqQBIphQaf0jh8/CSmmHfOnBfPXP+qYk+r4TMGMl1ucEZBjd1P/Q2fAy0qAnCRRThSd7Yk0ZOP9rKBua72zY/F90OCGpgoASVdGo6B7W7Nj/jpBplivdF7e2ukAKCcopgLUSYieV86pD8ySarlueMffzsvAlu1V2+4fSQAY6j8H4F1c6ncrAbfv2Ay6BmttaHKqUaugdesUbaS6HFUnZ31t2ttdnaqrE8ymSs8pPapTCa4PcDMDJQnVpx8ZlEaYxlyTNmwTtQpqEtQaaAt4QjD/nSVVY+OnBB1o1I7PEYxYbqOgc0eXInmQpg9BzhN7BKfamHZegOoUmXNqjwiC4eNy5mMET6bjs0la6zwtK8IQE302IqgNSQy8jABMUvKZzMNvUSnL8ggsFs/y43u7t5DvyHDlclm/RQ2b/J38ZnHtd1tozMjv0d/I72RuSn++j2oEfLZ2sjpH0/Kev6s2T4tjad2zm7fPp3J6lPzJYych6QCSDxzzdglm7Z+B/HNJyAuC0os5LNw9z4EABU0qQKaYRipn3qQC1CfdwrG5m2ZW1w6UydyNjt46SJsp5AqOlnNBwTF9g6B9S7PTLtMByhR2eUF2fdrR5FRBMidoSuTRf+icjv1D1rWGTkZrUwIq+5igXhv/Q382DcAcg7z89eex9lOrnU9ANnKzoHXnFNd4HBJ4laq0scW983PyDesTrvFoKFR3WZzKyaJBAnXyyUUfaoXlmKtR0HFgimoXqmVwpmGl4M6f3e/Q9m6BPClYijsUADj+UjSvF7Tu6tD0tEfUc4qPHVAvaN9axLQtrQoCBWlCyOmjgNrHcAAolTjedLMAtYTN8e2Ndogxm4XMj53PkBKXTGUS1hiIaxLIqPxmcQ0smI7xLK7layF/A9ORaZkvGczyYFoCAuPyPnox7t/8zd/oOzNC2ncr24DCQIXPVn9qG6Pla3mMReysH0HP2oDx0ykCTYDjR49V6qjLg0lvpEFqmncKktuTTliQxuoTOHG2B68fe80ZAbWNE2jMuVmAaU+3OcbmWpNGwaynOiuzBq+/fhIHXzmi2kJT2ODSNwpmrJvutF6uUyHN1Qs6NjToUIBaarokaEznceK7Ryv1tN/LkL/J2i76nv3B/ov+5uj3D/X+B+e/B7wDvHX+Cr5/aRCbd2/BI/9qrS6AWLh+GZp3tKB+VwH1Xyth+sbpqq4v/w8Pov25ZnTub9YOuu+5u5HfKmjdVnSNrvPwWRQlrdKfFnkCQGXNNxdkrBfIYq/+UwOgtfUewbJ/uh/db7diBe5TwyCNQUlqCuyUOYLSs+1uLJdz03zaeGVB07ZmN2eb5erFFmfkodPRiAdgEqwRNaUrmY4EyU5jaN9upEOMMS20vHp6elSSmtrN8ihlWQfG4T2ZmRe/WTrmYwBgeUZDEhWZjWmYlsMK5sl3fCaokYH5nczLfPmePE/9yAAAIABJREFUksrisU5GnNYGbBPWielZfpSw2XYEAItrdbWQGtW1AIBlRdNa2ayXgVcqFbpZKE71zRBM3zgTU3dOw+J9S5zKTmA8eBZHTxxFvsxVfRQ8ziqfoprfLJh3YDY6dza59SscajKvfAaHj53GG4fOIimBtxt4cEwLZm6ehvZdDejaWcSsLS0Re5OLQ7vSG2fPQDJcd0AX9NQoquDKNmP/2DsbHrE9or/Zvn/o4d+deRP4FfDDc5fw1sAg9v/FAdz9We8clIzKiwxK1KX0p11gml8txYamyk+LLS/eqw2ArrqTKEoSnJPXlVvmpJONVRRM3zkNqW1pzH5+kcuX04gEgaUCWetDluXReNaGBajfNhXt2xf7jvSrwbgrkOUynsYNEEqDs0Mkhkv/aMeQ0OwyVZvP0TjX0zlR5uQ9iZv5GpEzTxICn23owXdRBrNyGa82v9rnaFy7t1WOjBu9t+98z99cK/ntPePVEqvF5W8xjYBTg5anhdF0tCHYewsJPGarsHfMk/cEAA59LH9dWGar/Tju55ieQ0b2N6cRJY3DRw4iXeB0s1uWrtPXtDeRNqlBkC5Jk6QNDqGogWUzOP7aMZ0pakkkVYukD0qN7+1eukqV9G52BA59jn4Xb5w6jMPHDiPM0x7GpcSu7mR8A3X7XQzZz/xdRmPRbx+J+384cwZ4+228dfG8egfetW8vHl37JIRqGcftVIU4VcdxOC9jNKIp36cSLg7f83vSMSYX4dBamxM/9cdO0SXCbp2AprW80oIEp1Ro2GGjEwjYcSyD6XixEwlC5RBSl9KO4bLkClEwbtb5MUxLCDU+qgFydBAw5qrtBDJB7bvJPDN99CJxj1WW5UvpQKK38aO9t3TR/Oze4owVWrxoOFZce8+4xozRd3ZP7YLagGkoBIVo/ryP1tnSjRcy3ehx+L46vuey3LBAB7WCo+dO4ejp4zpU1TUFIadM6VyW3p897RAoSJOkYfU+HeLk0UN4/Tv/O7KMYwt5CHgqxWl/8HRGIGD6BO0TZSQSSSS9oTmjexhyamwOdQFcVQMY/Xd8hL///fk3gHd/iaFe7gUYwO69+7Fm9ZPIBHld5uu89XLzhGskLq1lI5PJuNkmoZt16iDsRDYqmbIS17bzhg5MFACYjtN0BaSlqGP1UNjInDqk4a6gC3+SUkTSj+OpaunwgdI+QQtu2ZXF8jywUDXTpcAcc3O44Rcl1doAjGBvVUdZ/qOFkymT6aPMVJvfeHnVxufzeGmi31k2wYASjNLL6sM4UW1mtHLsXTS/67/nDlS3eIdz8PXJJhRSJe3/ZM7Vj8zJdQVcpce9H1qWNzoTFBK6LiQFzhSQ8dMpQZarD3XY4GiWZbg1AhRQXrAwDykiUABIIFGZaRIU5BMCAEN9A8O8A+/etxsrH18FyTiG5nrnjDI0G4wWVrfDjqo9L0VOz/TK/GRIqk12KYNGpCKHAiolw2FMSmBh59F4FyowOCu+jrPY8H51n5PuHlCYNzuLY326KeelKw/dgiR9r6ARKd9L6OsnyGujuRH/aOFoZVKKktn4zULej5Y++m60vKLvonHtPvp9Mve0HTAPAoINWwgKBgyWf204mTImEpeCJ6N7T0g7FEQUJildQ+A2fVHbIyPTQS13qDqtgFb/vIJAiELOLdF15bHdHcBQ4AgFjgkVbik3wzXpjJotVyiat2yueOV0t21JjtgBJvJbPjJx+gcGFQDoHZjuwffu24mVjz/q1Puk2/lHdd7tiTYASOlSWxr3tJHYaNYAbCybo7WQEjzw6My4RFZl3Ahj8twBBQGnCVTWD3gkZx1sjb8uJ67kQ6Aiw5P5M5Bkyl0cV+qhIfweKecjBgBsNzMUmfpdy0ijPVfa29q9JryeNKPlGR3nW/1q441WFt/VxrsZz6ri6z6PDFJ+yze11OquT0p8bhXmblQaPd0QIiPUAJIIk4ETbrpWhTaMnG4NTigAcHOZDVW9jYn0TGHmAUC1S6Vd0pcDGwcCER6o6Yub8btvWR7uRKD3dB0AhwD79u7EmjWPIsEfrYeAOBBwYyRKJoey7Aiq3VoxIqVdxpimgvHZNASLHw0tXSUOUdlf9s1rGlzxxcvqUilT00Z2Hdr240h6a0Abylho7z9q4a1ioI/a75xsfVy/Vb1POa0xarx1tOMO/ajSkrmt1/KULvjNGQ4JGLzc1nUbEkS0Wz+DxWGoXgQ3ozmj1ShNf5zuL1+yE4Euqg2AALB29aNI+RVWxigW1qL9MCY0houG4zVGNO5o9zc5vf0OCydLgB9U/BgAJi5RjSZd3xjTTzz9RPrUyrCwmubWlFfN/+b+jhH5VgHALQWOAeAWN/h4gBZ/vyVDhxGEH7eza+fhAOCGALEGEINAzDC3CQ1cHugBELEB7NmNtatXIRW6A0BNVbbQVCALRwwBbhay2nBgvPwsnoXjxLffYWFM6LcJoY9DF7ctHcQAEDPAbUv8MShAxgOAWuKg5Oe0WuUyyWvhzWrU2vzsebxwnPJN8ltY+/vi5xgQbysamCwAVBjfQKCWIcdhwAk3ruVr+dnzeKHFHyM0xrdwwvUZI784fQwYH2sauDzQpwuBLvmFQPu8DUAXTESJ3jOejf0tHO/HG6ONFY6X/kZtDGOVa+/HLT/aBvF9bKH/pNFADACxBItB8DamgXEBoFblNtXfwnEQ0SSthdHVfHw3LvFZ+bai0J4tHCcPK3escNzyx8k/Tj+BPozbcHw6/7DaaMIAoOufuYY/YgDk/TgVr2W8GwKA0UBgkuXX1me8+sffYwb/RNPA5X63G/BSXz+Grgxi3569WLt6TXVfuEnaCQLAtRiM32oBoDa+PVcavbZ8e7awBgAsvYWVfGrixe9jxo5pQCA3GwDYqMZ8DKONzGcCALcYM4zGq72PplNDoAEQGZ/5GgDYsy/rmvnU1GdYGfG3YX0Vt81w2v3EtkcFACqzADemAVhDGSPaM0O+I/NPBgDcNmTv7tmGAGRW3eobAYIaAIhqGtE6xPe3CWHHgD4xQB/qd0uBL/f53YA6DbgGKR5lxUaMSlreV2wA/tANlcC2I6rql52My0MZHAM7ojMA0D3XPHqJR4Ix5LkBeh5AVDPgls8kknTjRMbn0U48543HgjE+z4azcwWidfQgwe2f9BugvyEmhokRQ9xOt187qXvw9+kenLsBB7Bpw9P47KefRDGbQzHtDkyk1MxnvR83PXONp6FGDt4IeCADD/KgD0DHmDz2K6un+1SP5lZPvSSynGDO+qloXJfF3dtmu/P+0lXtwM4ZyIQlZMUd471wx2IUttWhvLvsjmnmgY/+oAYFCDI+yyY46LmESfUSpAAUAQg9P451mIABczLagp2QwzQ84IOn+9gpvJPJJ44baygfKA386KJ3DdbrDgV9/oW9+PTnn3BSl4d+krF4UCedftCFF5mLDMXTUAgCCToEtfP8Uo4BU5Tk9A/I472qAMBDRFQi07Hnl71bMXoFonRn6D3AqEfi+f5w0GwIKQfuNOK5guAln46HNkYPHVGmrgKAeg0yDSQCANRoeCpsqd47ObnJUk+XStPG4U+6/UA78yb/lrjutwEYfe/iIDcD4urFfnz/8gC279qAFb/9kErXO9fdh/adbeqQIbW/iBk756rKbkd9k6Grh3nyOC7v043AoZKYU4buBCEyBuPrcV70w7a3wXlc4Wm/PHqczkGWCJa8/xC6sQjBe0lM/fF0957HOlH1bxY07MlUjynXA0l57FNaXUsxb9oXGPIIMYYjhjGJANl8DkeOH8OrB50zzZtB6NQAeKovT/eNmf82YJxPCth+r+eyB4BefP9yH176y/24+7E73RjbGHOPc86gPgH4jszNi+Nwfxy3O5fPexTme6+KU9W2k3mp2rcW8pquYUu66hqMfgYWChZiDuQLAvmq8wff/C9NChKB1DtX0vWCrm1l56yB9gN1D16CJBPOnlBwBzcSoHgk+agA4Dsuk8vi0JEbcwZqwEHmt3uea2/3cRgDwUeeBn5y8Tjw/s8x1HdKvQO//OJ+PLp8GfKUulTN2wSNW5vdOf00wpGxKbU5LDDHngoE/gx3HtBJTYBuubz678Ah0KGDenZNUwPwY3keutgiWP4v90J+TyB/KJDfF8jvCOQu74lY6pEmCKQF0ze0ek/ANDzSA1DJOXR4Oo3UMxmtM8sYDwDYMSffOFVxdRU96vpanUZNJhqX9+Y0g98IAHZyLvPhO2oEtVpB1D5g6RnHTgZmyGemt3zs3urH59p39i0OY/CZEA383cWjwPv/iKH+ExgauoCXXzyAlcseQplHKlOVbxF0ru92BjfaA8qCeVsewZRdcyCzBW076zHjmU4HCnTq6JnfDQ3oIZh2Aueii7YDBYCMoHtPg1Pl6fZrtmD6r7ogXxLMfX8aFv1/c7Aaj6irMNU6pIS0NDoAWN/pAYAd3ADhMIBA9CeC1J+lVSOhn/gxhwAR1Y0AQLWd7q94TZSZyJx9fX3qJIMORs3vG41/5vGX7+gtxjqBp+uS6emOix57zSUY3zEevegQPOghiK66akGDzkP4zdIx3yiIWDlxGDP+pGjgRxcvAO+9i6u9Z3F1sAcvvrQfDzy6tML89NLTRKeb6l0lr+eoq1ffLSFkt0DoHHSqOBAgYHBI4M/ojzrnoMGOJ6qaBlABAGoVc+kKvAXhzwWyyNkCZLVg6a9XOS9BAb3BZBVk2jd1V909SQbpZL0DGOaTpdrP45+zqv5zLYA2RtQIaO+8BsDvlNi8yLTjNR4Zk/HsKG+CAZmX6Qkgte6hyMx2tLZ5I7YyCDq8JyObazDmx3ysLtQwmD9DG2oQtHg/UcCy8uIwBocRNGDegd00YA+ef3k/lq68t6L+k7kbtxoA0B9aWSVx8kDRefKl9b5N0LWzXHUPbk46dHqQswDUDJzVnmezEwym7mpzswocZiwUtPyqAfKb3hMs3YKtFbS/vcj5IaQfODphLAtatkx1AFBHr0MppOlbns4mAzfmz0saeT0TPrIGoBYA+OwBgAzNe4YmvUc0UgQ07Ju587Jny8MY2d6TyU3Ft3dkbvqL6+3trQAOwcGYnyG1AoZMwzwo+fmOaXlfqyFY3nEYM/mkaODypTMAfom+S2dx6Woftu7egHvvvxOlct75Rmuj6+3paoWvzzdBuDCnTtB5YLaz0NM6XxDM29PkpDXtA3pWOq3zWTcNyKGDNwo2ZZt0ONG1sdMxMpl9huBuzAOlPu91VmCNoPPtBWoEVH9wZMJ6QfOWOW7MnwlRlDqk6QPAS3+WQSAoCt2acRHS6MRgjEWV2yQ5Q5O6E2lAk8iUxsyPUp5AZ2o/JTSZ1ADBpDcdY5qNwHzssTwCgpXLdAYAzJN5mLRnWab6M56licPR+zpul3Ha5fKlcwDeRt+l8woAL/zVs04DINPSOWKzoGvHdGexJ7O2BnrftKHdzc1Pd3Gan/EOPcmM6lDEeWah+yb162eLdvyU3rS9M5zGQACZI3jwV0sgv+Xu6QueYHDveyvdVCGHH5zzLwmat85wU4JZegpy7q4JGB3bMpi+xRkKC1KnqxBH63xjPn4j8zIkQ1FKm2TlO4LBa6+9NiqDGeMaU1NzIDPymXkYszKfb3/72woyfMdvfMeLcalF2LMBABmccc2NOL8bMBlwERxi5h+HsMcAf2vvOPTtd7VnEHgfGOrp15WAG/evx+LfvFcXAM3deB9adraieWcZzX/ehNmbZisT3vnCYpS35FG/Ia/awAMHlqC4RdCxteCYMyBzpvXSVX1kXj8E0IYn0z8tEC724RCCawAeEdzx3gLMeecudP/TEjyIz0DudUbIBGccaFuYKmjd0eCAqeiWDVt+LduLaN/eqnaAlK4e9MuSr0EIlKxkNDK0gYEx1lgAQE2BccnMTGeurMm0lg/H7GRwxuN9dOzPOHbxm2kIBADGJ3NHjYBketaJ9WHcCxcuVIYGMRHHIHDDNPCj85eBX3MhUC+GBvuw56/3YeaaRW4FIJfbkkG7vDbAe67A66zxu854vLy7bxrfipJASZJqjXcrBynF/fkBRcH0HXOQ21jA/N2LnHZBTYLTfisF8phAlvopQGoUacEdT03HtPWNmP3MNDcjwbIMWKipcOjBd2kCA42Vfh/DNQCAkj8qra/VmIzHy1R/i2vquD2XSiWUy9VVhjbEMGCxePX19VpHk+oEAOZv8YzxGVod7R3zYL6W1vKMwxgQJk0Df3/hOPCeWwdw+c0e7Hl5L5Y9udJJ7Jxf2Ufpy4tWfl6c948u9rG1AWTApDPGcTFOnQSoU6t81T24umBO5CDZwOXFtMyTwwsCDW0ABAOCjF90RK+slUVHjJsRJJOi/toDDi10HYLLh95bOQVIzcM5G+VqxeEXbQN2TabBjBGvlYZxeJE5jXnt2b5FQ+ZFbcI0CsubQGDp7R3DaFq7j36P72MQmBQN/KTnKIB/xOWBE7h09QL2vbQfK9auUkeJmYDTaRlk1QsrfbS7HXZuSS832/A7x9t5J6VCt0+AzMfLefSlJ+GUswNQAwi4NqCIUJqQlCZkpex2/HGIQDDgeN8bDN0OQeeElKv6VJMIypBESfNP05rPdB50dO4/qLpwrmX86PP1AMBEGtaYshYA7H00tPwYl5oFv/EdQwMAi2NhNL3Ft29xGDP/pGnAXIO5WYAeBYDlT6yoMCNdgFOSc349IVm9uM03ut6e6+/J8GrsI0NSKvMiIOj6fLc1WL2v0nKd8huJbEchwzSXEQcV5ucGI9tMpDv3CAqqeaQgGa4LcMCg3lrNays1BV6sg7+371Hm5/1HAQDIwLZGgCAQHS7YUKC2Q2MAiJm8liZu6Ln/sjsPwGYBqAE8/PiKiqrvAMDNuXNaz13cfJOorLYjGPAiCFTG5SbFA6rbdjZAEpJ0U1d1ImgQGgu9ZE+RscPq0EJyCKSMMJEHZxJYD8ZlmNEzCbi6kNuQnW/4CuPbbAPPF4i4db4RACBzTrSRjUEnogGYBLf8bSpxLOnPOlj+Fk60XnG8GDhGpYGr/cPXATy9YT0eWbXCSXARNOfoN903HpmXkpqLcqSAtF5uh19atQSnwmYTgoLGGaXRMzlkRLB1xjxsb+rElzpnYDrX7pcLlTK1PH/+QCpTRKME+NqUB/BMcR42tc/GIoJNkISkuN04hzSnFqNDiJQDpJy4HYi1zD/sObIQKDpNxzoYY44ljSvtYu0TCY1BTapTxbf4xvh8tnsaATkVacxfa1y0tHE4Ck1F2j1un0m2z9WBkwB+gZ4rp9F/dQD7n30BT6xa48fvgqkiKNu2WjY0pXQqCwnKOpanqs7dfk4Sp5AJ0iiHObSo7cBXhuo4x+sJQaa5VfPb39CF9SJ4SARLJIFGSnYRtIkrc6YImjibkEzp+7XSjN8QwYvl6VipGkcSki0qEHFFoAJAxH5AQJoIABgDRufdyfh8T2a07wYGEyUwprO0ZGYDAt6PBSi2FoBlMH4UNCZabhxvkgxwu4NH79BJvIef4/zQKfR+rw/Pv/hv8ZmHV2OKCJaJ4IulPJ6ZNk2BoEhJmyhCUg2QsAAJc5Ckv8IMJJ2HZOpRkDLmSj2WSLNbjUcAsCm7liZV4zc0teMJbg8WQb0IflMEfyqCH65Zhv/rwTvwy3sW4//+3c+jM9JBBKJtrQ4AVAPIFV19ghyEEjZNIChAErycUW2YtK+ZDeA3YxjOs1MC2+IeY17bJGTPFn+80ACATExmNolu6wts3QHj2TeuKWAd7HksoBiv7Ph7DAITpoFzV0/ibfwCZ990ALBj5348ftdy3CeCP2lqwqdFlFH/dVsX7pQs6v1RX07lp6U/1MvsACJcohtildTjj5oXqUSv2AZoF0g5A9y6zi484jWL5kDwNRH88t6l+JYIDoqgXwT/vHatpleDYlqQDwTrOqapBsByJc29CdQCsmpPoE2BQxNJFp2tIekt6qMwvgEDG4rMaBLeGJ1LdrnwJrq0175NpHENAKJxv/Wtb1UAh+8tb4tLho9qItG08X3M1LeEBi68+QbexS9wQYcAfdi97wV8+p6H8dXuWVgjgkZJoklCrBDB082teEAEd4lgsQjmiOh4nM93iIBq+wIJsFwy+LwItqTa8KQksMSW7HItQcrNIDwzZYqq//xRlPL/efUTyvxHRfAfRfCCCH7bG/1sRoHTfASAx1RzoDGR5wUWkZcEDnRMwQvdU1SbkIw/mowAoIeNDl8HYMxvGsBoAGBMaZKaUtxA4lodYeksZFxqAZTqzCsq1bkikHlGL9ohrlWO5WvhteoSf4tBY1wa6L/yhm4G6r90GpeHBrDj2efwqXuX4+kOAgCt97TCZ7CKhrv6Eu4RwVfmLMCXuhrwqAjmU1OYOxN/3J1VhubzH3TMw55CK57LtuLpwiz8/vS7neTTxUPcris6rHjYq/ddIvjpQ8tB5v9vS+/Df169Fm8tfwJf0ClIP3zQ5cWCp9unal1adcORk/4FSWBbUwue7epAiXlykZGfhrweADDmYmgAwKEBn8dr0Gha3tuQwtKZlCfz812U+XkfA0DMtEYrH0j4Vq+bBRjqPat7AbY89xzWLHUAwDG6W9EnynRfa61HO2cGKInbG1QVL/opwC9OKWK5iDJghwSqAexvmaVaAc8A4LSf/iA9RFTw1JRuBYzAaw7/dXEXfrZ4GmaI6PW/EhQeXolupqP9IHB5r2+dqhpAHYcAaodwG4IIKjQiaty0k/zuzEJKfxopR9cCWKeJaADXAwBkaDK8Mbl1KDUC5sfNRvbNwloAqAWU2mfLMw5j4LguGvjxhXPAr9/GDy+c1UNBNz//LFbdvxzr2+bhs56hKVWpAfxphzuim8z856U6/a6FpgS/15bFas/kZGrePzttphoBg5ybRy/SaJitQy6RwaZZ83SIwfTM71cPL8D/ZCAhgv8gAjx4H2YbU4cOjNa1dinw5AgAKRois5CwOsWmswGU/gljeDL/zQMAMuC1GrqWQaMqv6WzPAg8vDfmZxgDQMzIRicfSPjjCxeAd9/Fj8+dx1uXBrDh+f1Y/cAj2NV2Hz4jCWVOMvRaEfxRg1veS4m+qa1LLfdayaTgv2/N6awBn2n0o/Fw99QmPaU3ybG/Tuk1QhJcOixY1zkXT3qGp/R+97Fl+KsIAPw7Efz8wYU6+yD5pO4yZL5fbu9Ue4QeWRaW9ICSpGTVJsHhCRcKqfrvFwSRwcaS/mYD4K48k9TW6MaUZEhK7CijmpXe4l4rZDqbAqTRj3kxPt9zRqA2LbcPs2yLV/ud6aJX7ff4OQaQSdHAD3ouAL92APDDgQHs/cbXseKhR7FGWvHnnXeBKj6t6382r01nBpg5l9GunzJLZwc4HKCG8OXOMmxMT1V8ZUKwcWEXZvn09bq0twjJNOqqwafKnQoqzI9rDd7+nd8GmZ75cQryeRH83WNLdS2A1BWUUWgroCGSxsk23fFHQGkETxn6Wlc71nU1ufgcMhgATMAIyDqMZn0nE3Ksbsd9kfEYl4xrtgE+j3cZw9oRYDbHT3CJpiUQRZ9Hu7e8LBwtTvxu/D6J28i3kbkGe+vCRdUANj+3F49+/jNKiGTsr02dhW1zF6l1vciDPvy5fneK4KvlRvxxfQO2Tp+CrY1pPDW1VQ183PDDBuainj/uKOJr0zvQopuDSpBsvQLGC63dOvW3UESB5SkR/GjJvfjpIw/jvz30AP7L0jvxZX/OP08h4uzDH3J2IFePz6mdoIgEjwVP1OsswFMd3djQ0aE2imFLgPVwkrG1ANaTc+8EAGNwvqO05sIcHtvFb2R4k/ycIpwMAFCiG8HxEBAyfq305zZifqMmQsAZbejAPIzxLbR84zBm+uuiAQOAod6LuHplADue24MHP7MW0lVGOiE6V0/JTjAI0jyDz2kAnLrj9B/H+lyZx5DPGQkQFFog6axqD0zLaTtK74yfDqSGsG/hIjxTX4/f6urSpcBMTwb/X0TwEsFFBEsr0jWFP+6ejS3ldmwttesQoFuPGytBgjxyksC9flUhtRUCAIFKw3EAIMpoZGxjMmvM6AlC9o7hN7/5zQpTR9+Pdc9yogATjUeDoB0MElX/o8Bh8Y3xLbT3cRgDwHXRwA8u9gDvv4dL/Rd1GvDACwew+vHVStxU9blE1y3TTYLbbzkrwIsLf7j8l+Ny3nPszYvj+2SQVos843GVH8GDdgN+c8eGuzz4nun5nt8Z9/9v702D7DquO8/z9ld7FWpBFZbCRhDgBpASuAEkNgIgKVKS5fCEx/b0WG5ZlEWZIEhiIXYQBEBtlrvbETMR/WFiOmZiZr44NBZpiVooLhIBFIDagCIo0rRlOya63Xa3LbXcFiWKPBO/zHteZV28WrEQqMoXcSPvzZvby3v+/zx5ckNT4CJP/Nyf4jgvt8mInx6MZkHalE/YEzDrbRPYEhj2wxBYWQUIAbAoKNV3tmdAZhd+5GdutQoFqNWIolrY0M/AbPmaG4bh3vwn6qbjx+dIBJOSgXeqEMDmzZ4ASChLi5/NjgB1mXn9LOkt1anU1KjUsJLPj70juLTwWPYBpDtDMOsXFDnA2pTgAot5iirFrL/cs59KLDX1fgMS5vYny3rdHgGEZZ5+1m/+yQag7r31+d1Mw2ECqGgAYxBANaCNV4HEIcxYrfpoaVTL72L8Rssn+kcimJAMvHnGawB0ATgd+OCxw7r2gWECAMyo2KjvXK7ldxtxMAxXUikkawGyJX8eAMNvyRbdbicfQGlLgw3M4doAW8CDnwM0S4bznhTcKb++9XdAt3X+bolxogFYmpBAsi+A5U9ZnYYxCQIYq9IgwnBEYKywo727GLBXiztaPtE/EsCEZCBtA4AA7n0wIIDMMAEUpdZv851hEk4mad0BPmv3uTgFiANBh9fi+5Y7scon9gPXFQDs1nIDbNdXT0DNLL9cXiWb15xkHem4P2NgTxMAaXHRKifkg/Z9Iz7OAAAgAElEQVRxqQnAADihirXuS8q1NC6VezFliXEjScjZPr8hyGCv1wCOMA9gywbf905aUFpRP6su5zb3cKq8638b8LBye0t3RbABq4Wx1j3ptxM/nQbPEAOXf+fTvCBsClChEIdphGn59OLHDusq3kd5cDIw2O8JACMgXYCjRw7pls3DBBD2o7k3QJqbFqQKAVRmzBk5GKA5sWf0a1TgBq18mKeVw9x0fPMP48T7KPxRBhIZuNQEcGHFfrgEcGF5ovDHOokyUJGBSABRGCrCMEb3KoaZpnJyAQE8e1i3bBo2Ak62C3ChoFwlGoB1IdJuFPqKvefCbzdNhT5+8+FvHgkgCnkE/gyWgctPACMrN20ADIXPDHbmhu/cMF8y1DfCP2Bzi2fuiHDplt+eg/gjwkf/4VYi1sX0rYuriQAAYFXwIoATBOy48S0dc6NwT1/hjt92/G872N+r/Ab6zujQ2UE9mrYBpHbSMYCZe9lbTQPqaO54H3m0eOY/Xvz4fnwhinV07dZRJICRXZTLTmgRLNcuWKbjt7vsBGAtLW5SgWgPdl9R7cNwV/I+LEu8H/4usS5mRl1caQK4oOtwJcFeLa8o6DND0ON3rv6dB/v6vQ2gt0+Hzp7To88e0S2bNlcCp/fTMwCbW2nJR6tgQFdlLUAlXjVQXkq/0coV/SvfuPItYp3MvDq5rARg4DcCCNYSVIRuPLCbUIbh8GPVYehX7d7iRnfmCXb85hP75hUCqIwCXKQGANi5+ACA0oE/63fumSwBuGFBv3Cokh5pkjbLkS0vl0cwVGhhohBMTAhiPc3cerL9AGw5sB8G9F0A1PzKVOBkOBA/33oDan9v3QH3LgGl90uAz6aYbN3lVgEm+wDUiUqj+J1/2DCEXX7cSUQAnh2E/JXDJR+2Fm9OLjYRqUnSYU+BZDMQRwi2aUiy4tCX1coc3eleH7b12nT/n5fs/73NyUAf/FzP9Z50y4H37dnp1gI0lmq0nBXNA2iOCK+tVRF/sKcDJBt2cLmNPLJaEL95h7XKRSkqG4g4IEMAbmdcSMCDecETi7TxsQa9aesSf7R3VrQhV6f1UtKi+F2FJdfsjiZji+/Fjy/Spt21Omt/o8ocUZmV7DRk24CxDTj3EANHkGXYr7DkDgUJlyjH+wvPFbAzCGzX48kIlwGOep1oPOLYrsp2dFq4OWt6x+SJpks40g7TqhaXvK3c6ffsBG3xrV7SYabV8zunTqh+8AsdOnPS7Qr8R197Tjd9bINXrwEVgG0RlY4EdLS2+OUANa20Bz+AZ/cedzJPjm28OASUY7vY2SchAKcFiEqDqHxOVBaLSleiCdC6d4oH92xRWSYq3X5/v2xbwWsLy0ULzyXx2oIDQJIzANxZAAkBZDI5zUshEsAom6EaEfItw+PLpyLcxG9qapoQAbAFexrgxDci4B3As7MTploetlkfKy75UJZqYeyMiMmQWrV0rgm/N0+dU31f9fypPnc02KEju/Wuh293B2ss/8Kt2rS9WeVJUdld1Dk7FjpVnO22bOMND/SiA7z7w9YSQxSo7g78fnsv3w0QlVbR1oNtKosScsG9RfSGd5fqTbpMl+g8zfxKdN6PZ6nMhQSKvlVvF23fn/d+EIbUqORKKtmS246M7kqGfQRz7ExsOw6PbPFM8K9ll9brUpWfb0bLP1XAUQ62TqflfPHFF6sCKg2EEGC0toCf/AkHMI0MptoC25kO6Xx5pry4VoZ0mGoElQ4zrZ7fPD2YEMAZ/dFgr/7xn3xRb7pnuVelaakB56Gg1QV4BnL64qjbhWAOP31wa5HpPpimgLaQyWtzXZNLu3ZnnW/xyQN1fp1oWYsqD4vKb4jKE6Ll933+NaVWL1izRBfsqldp91pETlpVMpw2lFNpEn8VRdm1eKz9APmAlxJEBsZqaiV+lzqvaulV87Nypd0w7Ne//vUJgXY8oYdEAK8BbLTwHIoymoptZy3U19ePejSafbvR0scfAvnmN79Z9X8ZqVCG9MlMlib/wboo5jdt3R+feln1g5/pUO9rOnTutB4+tEe3bFivtRy+Cbjnirbt6fSgoysA6DHeoabTLeCynX2TxTxUFt0BZ8wD+MkGnxBAVjIuvNMAaN3pt2MQXC16n35MZYWo3C46R9tUHvTdgKI0ar1wqpDo4idbnQaBUTDHyUCZJl+GbSXNPlV2JAD4QwII5zLYh8w7m4TvzhhAeGf3o7kIRnh9+9vfdq0f4U2wLQ9XD7ncBf4mhBYOgSd+2h8/CxO6AJgLPzu4JB2Xd/YfKFdYNvOn1Q37vJYmcauFt/LwjrBhS80zR5tZGqOp1yGwCGtpkidl4X+k/wthyMvSNpc41S7C20Er9j9wucL87Ij2ammMRg7Vwl7Tfn9z6iXVD36qQ32v6NBQjx4+tE/vX79R3eGbgLNLdB6qPyDPZ5wl/vqd9+r8vUtVlop2Pd2gSx7rGN7HPwG/NwoWvZ2gYjCEFDJOA2g92OHIJUPr3+qJRm4Ulet9///+f9yicrMnmKLUa700uzIsfmK21xgcATSrSIPXJD4nmnms5MgJ45/fyDQZxUiNYNihoHw4DvngmG7URtRCBGS0a7QPHYYfLQzgQMB5j+C98MILFQDzjnMDIRPecUSYpZlOz8AHCJ5//nlXbjtSjP9y+vRpl4bF4z/19PS41tnS5R1h+c9WLitbGI8yUR7Kgr+RDXG4eGcEQrm4p1yWbjUQTYQArAzmkh5lD7sYViYLE7q8gwAIj0sdGAGE5EK6Vs/mkg7/wQgkTHda3r9zqkf1/ff0/Jnjev7caT30zB5du+Ue3wWgxV8k2r57jn/Ockhnxrf+O3Iqe5MuwjzxJIDGUKY7kIwIYBREA2Cf/7w3BGYTzcIRANb8Wt9Xd0QwT1RWia79bx/zRkBU/VKirmeLrnWfv2OOJ4wG8ilqvtSkUsx7UqgnbFHzUuNPBE5OBUprADZsefyHr7uWhdYFwUBtNEGo5o4mAGHYamEQPvwRREBBXgiZgQ5gIYxhXMggfLb7hoaGChhJF7Wbd6SHayBHJTfA8P8oI0Rn6VgcgGzlt3dWLnsGtJYGaaI5WJ89TQCkRd6jAWg8ArA8zbV0yJ90Ka+9q+YaSZ08edKFp44oE3VPeO4tXlgW8zMXcrP7ae2e7/W7AvthwNN64PAevef+1V4tp2VeRBcgIQBa22yTA2Xu2QanAbguQLvo/F2N3jhXj1o2PI5fGQVIxueznB1QEG09MMdb/Os4Bqysc7IdnljuF138/vVuBKCFvjx2BLM5tIjO25kQQL3vZuSLtZorld3oQz7HaUQlLUtdxfofgt/uS5xIxAGgr73mXISLCz8Dw2guQhNe43UBSMcIAGEG/OZn4CVfyMfC8TyWcFp8wnGRLoC0Fhcy4JlwANROJbb/iT8XcS0Oz0Yi1koCNt5TFgMgmouFs/IaoRGed6bdWPlCN/xfhLVyECZNPGE8AInWYoRg9RiGsXvStHDmZ/+TeiFfLtKze3P5T/xXqzOLP23dwYHXVfXn2jtwXAfO9+qOvdt07cbV2tra5I1qHaIdOxc41bqO1pYx+gbRrmevU1mQTMypEV26r8MD2hFAwVnos1KjtW440A/nMURYX9vmtISGpzt9372BQ0MLWictPv7Dokt+2aayULS5qeg1j7JoAQKpF124Y64fliwDdt8XdQZAuigFfyZgvTQ5LYCDSnKS89pAsK+BEcDrP/AqIB/XBAPhmeqFEKUFBT8DCuo5gtvcTNfFq+EW3gSUZ+IgwNXKwXv8LR7pWesGoZggm5sWaPwtLq4BknCWLmHQSGhxubf0CQ8Q7f+Qt6VFOADM+7HAgwZBWEvD4uMSnzRNy7H08bdhPeqQ+PaO7xamwT1pE4dw9sz/CeMRn7Km69jCjKdppPO8Zp8HB06o6i+0d+CkI4Bnv3pINzy8zvf5say3iXbuXuBcNxOvw3cBWp5MDIMLvRW/5bFCRTUX1Hyp04LUaYNk/SGftOSAmC4Ew4DPdvsRhm7RQpmPmPPj/utFl//EE0CxIePnDCTgp7swf1dXhQA4idhVfLNo144GXbi9wxkV66VV81LnhwZTBOAEIiGDk68fHyE81fqEaQEZ7zktCIQ3YSd9BNaEN1TJjQAITxqmHfDMPZe9S+eBIONnQCU/wpoQGxAsXBjfwoR+1npaPCMu0iW8aRLEodwQBff8P1zyxu5QDZykaURleRKesKRv3RbekS7/iXeE4T3A5h3p8M4IDD/eW5qUi3ISjrhWN/Zs6Vj40LWwod+0vT9/+pzqB6pDp/vcTMAnDj6ud/32OteaLnvqdm3b3a4tuxu0+Q+adNG2RU4TWHH0Zm3cWatNT9a6VnnVoVVa+1RWZzNnANJwB4PWaL3TAIKz/WwSEYa/J0Sd0Y9RhBrRfKnBjy7cLvrrH6xz99miaBb1H1sEcRaKthzs9ETjNA2fF6MS7bvatHPXPJVyRovS7o4qk6wHgqn+1vdnBMBNW07UZwQ3FF4EZqpXWlAQOPxoFQGPARsB5TJQco8wAz4DiAkrz1yUKZ2+PVs6PAMEwpIfaq4ZF0OAWDxc4qZBzzN1Qr685540ASMAAUCka2RGOOJYOvwf/MJ8uCcNs28A0PA95cOGQZqWLn6EJz3yxYWQiEcZKJvVC5ORrL7xN0Mn8UjH/j/h8WP0Jcyfe+KTrpFa+v20e37n5KDqr5gIdEaHzvXqvq8e0BWfvMNrANgAAB/GOob+MMoxA49n3jGGb3P0CQcoeXZHe5eSab1+joCbImwE0Cg6Z+8iLe4o6nK6F4zdN7Z48pgfzDkQ0QKLfjKiN+y+Veu2z9HOp2/29gmGDukDsyqQcpA3fsWM5qVFM0KrcaH6bx+wgEAwtTmbrVi3DXAIyFQvSx+XNBA6E8rwHfcm5Nwj2IS3sHafLkc6DVPT8Sev0cLjn45rzyEQ7d7KYemSj6Vv8cwlbd6ba3HsfdrlfwMy0jPV3uoCN2zVLW5YfuIRjjKaxhC+tzi4hMUlrN1DUnYfhuUe42Hab1o//23Py6rv+3kAg2+c1l2Hn9bVD25UKXP6bzLGj3UfYHMBMi6bc88sPazw5sf6AeGI8JzroxeFsf9hG4AIQ4NJ3x7QcpF+hhOBi55o0CLI2/q7dAEgILSAlqxKA6MK/ohw161guJI0in5EAduAnwZ8oQ3APmaoBSA8l+tC8EYTTisLrZVd5kc8izvRslXqa5TxcUt7LDcNjHTeY8W1/MM4lzq8pYd2A1FQR/hR7vHqeSrls/ymrfvj0y+p6k91sP8VHTjfo7uf2aPrtmzSXI65/XkHpLzrR2fd5B7uiw7chcTajkGLedcYhGhlYFxrbVg8lIwIAGIugO5OGU4W+rjpwsP+Iqhlvk/pphLbe+IC9GKzSqHRaQVZe5fx3YwRE4CcAfBCArBugLmhsF7q+4kKDUJsLaDFmSz4JyL8lvZk3LBOJhIvDH+py0R6BviwLPhZfYX+8T7RksdqEAYHelT1vYoRcPfhnXrPg2t8a5/HQo+1nSE3gFt2fWta13rJaL3zJxNYGNAnm3S4KcDJMl3G/9104GRBEO+4KgeEJoVkvgCaQabs1w8YYVh4ug/OL0kv2VvAf2TyT4gmwxHlucplApm2A1wtBIDF2wTb1G97trJP1L0cAh/mPZH0w/DcTyTOZMNYupCmtfyW72TTmvHhT53txwaovf1ndHCoX/c+87Te+8Aar9IXfMsaEgALcCCAOhF3sSjItdSOZRICqIA1UeV5TvYDsOXCngSwDyTgRTNw6wXoIhjYE7IwEgjdEZuLGAEUVXIFfzkSGFbtr1YCQACtVbPpsybMk3UvhzCHZZhI+mF47icSZ6phSN9afst3qmnN2Hh9A/5cgL6+M3ru3KDuO7hHN25e59Vtt0kHrX9iyBP6s954ZlNtXf8+VDFMLU+BtUISvOeqxAG8diWtOM/pcOnnSnxLy9JI3BF5WJhrw73cwBmu+2ujPsYrbwT/RXzH/hQBHDiwTzdt2qg55v1fADI/0SaTHXarhZmcXwq4pspXSOEi/lyV8k+ubB9O3pEAJlfvkQAmV18jMBAJ4CIq7xolmBECEP9D1YZuxtRRJIBIADNG2CPZXUh2V54A0ip/+jmwA7huQARoBGiUgcsmA5EAonBdNuGKLe6FLe7VVidXHwGEGkEEZwRnlIHLKgNXLwHED39ZP/zV1hLF8nw42sKVJ4AI7AjsKANXjQxEAojCeNUIY9QCrrwWcKUJwObgR6GLxBNl4CqQgUgAV8FHiC3flW/5Yp37Or/8BBBa9f1OPH79gPlHAMaWMMrAhyYDl5cAAPnIiT2A3y8umhgBcNzXBQuO2CiExUaRxWMdRBm4OBmoEED/Kbca0C8G2jT1xUAjVu1dSAB2pqBfBsz70YEM8NldaHg1YhAWArC8qqz8I2414hgrv/guqN8xvkusp2lUT2f7/LkAA31GAAd006ZNyp55BqLQdQdwuqW+Gb8fXxp8tgzYjgZLaQCA2a33Z3sx21OQLb2DpccFpyX4HYhKbCFGHMIH5/+5LcDIi70GuCxfu082HInCOo2ENZLSmA3mlGT9rTMcD/6eDvZ6AnjiiSf0oY99XBtKDdrAtspJpTew759rkf1xW8Jmi3kuiIA9Ajjwgme/mQen8xTd1twlFXbpySTvSa9G9Lpti7Xx8Ra9fudH/Aak9f48v2bJuV2IAD7Hi9eKP8L5ll03atOuOm3b1+iPAmMTUrdFWOLa/oUQhdtjsKAcEca5ALZc9HK4U6r0KMiXXpBjnU6tTt8+dVr1g/f13JkzOnT2nB4+elgf+LWHfIsKkGhZ2Q14rmimUzSX9UB1u/FCAuy8A7g5MIT75KBQfyhHjfdPCMCRBB+KjUAfEZUlSdpsMMqZgDx3JTsOc/goh4dyig+aArsQXy9aOpYcR8ZzZZ/AZOchCAECIL2sbQwaCSCSVNSCRpWB86fedMeDD506q+cHz+nOfTv03k9tcOC6eetdOmf3bC3tymr5YJ0u3X2dA1cjB0UmJ/B6UCetPK0w4AOEyUk9RhCQBGHZSYitxrsOtKssFhXOA1wmKitFb/jvy/XWny/Wu/VGXakrVW4R39qz0SjHkreKzt5XrGxTnpE6lVyNSs7n7wyDnA6U90RFXmwFdjlafktz1IqNLdLUWqRYb1e23s6ffiMhgAFHAEe/ckRXbljlAQzo2Kd/nz+Uw23L3ewBVtkynO3AATxdAS60BlPDIYREQ/AEkNO2On/Md9OOWg9uWvclosv/+XqV3xSV+0XlE6Lyu6LXfbDCHT+Wl0Yt5guOBBbubPRnE7izAVtVsg1+C3PKylUULWZE81wQQMbvz2+AxQW06b3kwveTuY8EEFvXa1oG/urU66rv/0I5HPTcUL8eO3ZM7129Tsv0vVHVO0Tbd8zyB4SwNz+gxp9uAVdnAniIgF2BIYERwKdrwOVtAGwwCki7DrT6lhxNYYHobe8uUfm4+ANHbxeVh0Vv0TXuXUmatTE5Hnzpkx2+O1CLit+ukmnyZww+UVJ5quxIwPYrrEYA9rFsI06eDfDhvfmN51p60Y1EcE3KwI97fqD6wc/1XO/xhAC+qOvu3qAN7M9Pa94mOv/xOd7SjsW/QfSm7Wt04Z4lKteJzt7bqAu3dXoLPSSQgB8bgLMLZKoQQEl0zv5239+nywCJ3Cd6sy5SuU1UbhWdo0tUtnhyKEqjNsosRxxLn5jjDwip5QiwVpVMg0/nc6KyteQOEMlh/EuOBnf7FyYHf9gHAtR2z/FRnNHH0VccFzUe4NPvLZ3oRgK4JmXg7VP9vgtw5pQ7G/DIc0f09nVrVGoyXtWeKzr7qbbkpJ7kwA5a/u0Zlb3iSIAz+xwJoPpDAtlkb35n/EvsA260IKNldvlJEwBHjW0WbdQmna2Lda5ep806y3cHFjDpp6iZbNmBe+GO+ZVjyRhpyJdaVEr5ih9hc1LjgWyblwYn/4QfKTzokj3mOaI7DfDxnsP04n0kgWtOBs6f6XeHg55zBNCrR754WG9fd6fvx3Nw53zR1h1tDrRZugW0uPSzD9d5yz2tdydn/TX5033pJjgCgATQAhIyQDPIMYLgj/Wat6/Lt/z4zxO94b1lKv/aq/7ykKj8j6I3v3ejOxDUaRVY+FtE5+6a77sebtiwoLlivWY4nZajwvKkX/LDjwxJZqsbAO0ADjvIkmfzGw/w6ffX3AePRraK9he/nagM9b+uqj/XgX66AL26e89TesftK7SlodYPv80Wnb2r26ndjXUt/giwBtGuI4td/9wZ3upEr98/21v0Meq5yTuM39cmBDA8KjCrptVpE11PJaf80s3oFL3tvW6VB0XlDlG5Wdz9/J91Ow2j3AKJeJtD595u3+ev4WCSoj/kkTkBdCWwJ+Twb3JagM09SIPWwG4n3iIInHo7FcNgFKLY6l/TMnC+DwL4hQ72nXSnA3/pK8/o6rW3eZYEzG2iDnS09Kj+jM93ijY91eGBuMiHmbW16NVwNIAMB4LWa86dAZjx9gObtIOhsEW0+9B8rzFgUFwoevc/L1H5lKgsT44Nv0/0hn9c4Y2ClAOAt4p27Jvny1EjWutmGfpDQ7t2NenCnbOddlInrZpjiDCZfBQSAB/LnjmyO/x4Rgj2fiJuGD/eRzK45mTg7R5/PPhbPWf0R4O9uuPgVr3tYU8AN2z7iLbvadOWfQ066w9bdMn2xc7Yd/OxG7V+V1kbnvQjBbc/c7vWb89r544WPxSXAZy17sIY51R4VH0m7qCC0mI/Lio3JJN9FojKGtG79Va9+b2bddnPV+pHPljvjIGQTZ4JQdgXFjN6MNvHrw/m+jeLtu1u187d81XKHA/erhxh5oYgg26AfZxwBIBuAMDn4v1EQB+GsTSjG8F/TcrA3xzvV/2l6l+cPKVvDZ7WZ766X5duvMEDlXF1ZuYxWYd7jHVoAQCyLTmymxYcQHNxnwCzTsra4KbzimaYn59MEXaV1Ci6YO8Crdme148cucXPNWC+wUdFZV1yMRqA1kG+NaIrt96kC5/q1mVP3uRVfWdsJN2sH4FA80BTKLF4qEXFjT5cOAvQPpIdKgkZ1NTUuP8buwARxCYfM8b9TydeUn3vp/rW6Vf0/LkePfTcPl27Za1X221SD2AD3LhctMao5Lwv5FVYJwD4CJNnAk5Oa9wBohwiynHiCQG4IcKCCpN6SIOLrgH+AB3AL0wu7ln8U0yW/tK/J8+agkqx5JYDMy3ZxbVylv3EH44v9zMU/dyDai12qAWE7yd7P2MEJRoPfaM43erhb3u+q/r+P+lQ3/d1aOiEHj52QDfet94twS1nWJDD9F1/IGi4KrAgWS1IWXPSqMLlJvvknNGPBThMwS1KRmskp2Wm8poWwMxAhumkQfPSpDVSpzXJuL3TEiAEtAWG8DK05j5/JvW4xUYZZv/Ncukz28+FzflZfxBNZfKPm4cwOgEYcCcL+HR4Sye6UXu4JmVgqO9EYgT8oQ4N9ejhY7t13Za7fMtaEmXmHvP+AbW37rNCMKu1Qj/fb+7BH3fgBNw2JZhWPef76ZX1/GYPKGZUioT1Q4Wur25dhLwHPsTDkJ7Ll5a+ogFkVGqyDvjOvhBMNcbo54YgbZES77J+2bIBN/2RzH+qbjq9+ByJ4JqSgcF+vx9AXz9TgXv1yNEDum7Laq/elz3464wAMkWVLOvz844YKgTArDvX6tPSMx0Y1T1xAX1CFG5pMcQgovUi2pK4rotAyw/IC4C2pCz0YUIPR4cTDyLiYp5/gTQcYWQSjSOZa2Dk4yYdJScYM+uviiHQPtJUgW/xLJ3oRuBfkzLw1pkeVX1PIYDBoUHd9vhOXb9ukzfciWhbbbBrD8AqAWw262C9f43fscctvGFuPlqCaCmb0RpsA0F/yboP+AH+HfOv02PzFusjXR16E90Dwjo3o1I7S6XAVOR6Zd8BCOjRpXfqjrkrdOvcxbqcsJBA2a8wLLPij7hGIvlh4vJdh+oTggBxWMZ4H0E842TgzV7fBegdOKkDQ2/oMwf/SB9Y9wmn3gPUBUlLDZBc5UAArNGXBtdK20w/P/e/oIVsURtyNdoqJddipys0U6rXThE9UNeh+0V0nYjemRXnh0YxN7lmJV2MUs53MzZJm35SsnqkuVvXspoPwNeiKfh8WALsNIjEhkC3BeKIBBBBnZbB+BzIRN/ZE/qB/kJ7zp7UvjfO6bEj/04fXv2QA/4aEf1MQ61uWzBPF4poE5N4snUq+Sa/Dh/DX74muUoqxVqVcrPWSJMulWZdKW1+/X/SDXB7+JXL2iI5faK+Vf+HRBuAZHaL6D/ccYv+wx0r3fXTu1boNhHtNuJJiOhAa7dudnaJrEqZsf6Stz+gETjwezsAi4DcUuDEmGgqe9qNwhAIQ1DXsV5mSL30DJ3Q9/QXevKcJ4A9Tx/TB1Zs1Dskq59t6dKHRPQBEf2t2V26UoraIiWtkZrhPrkb5stV1t+LoLLndL0066fbbtI5iRHRCRStdNIyb2vrdGmXc6JtIvpPa27Tb4novxfRPxbR74noL9fdrksQSob5sr41397ZrVsccWRVimwIwkhE1qVBOowauA1CyCs3bAdIA9+eo6DPEEGP5Fa9u3vqXI++r+/p6UG6AOd0//6v6MMrN+mjXbfoFilqq+S1TTJOVd/a2qZ3i+hHRHSFiC4V0ZtEdGXioiUsl4zeJSX9BP38wmx9SLK6SspeE3DzBgque7Fz/kIHZADYIaI/vWeV/on4rsBsEf1fRPRna+5xXQJpyLj5B2wW+uiCBXqviLJ3oLMTSI02i+gX53bpl7u7tJUPjSaQdAXC5cAG+tCNBBAJYEbLQP+ANwIO9J3Uc+fO6Z6DX9GP3bpJt3ZAAGUtSK2bC7BJRJ9urtdVIvr565bpI3OaHClcL6K/t2yxfnp+2ZHDMhH9na5lure+Q58td+i22iX6P3ff5nlfaJ4AACAASURBVOYVOFDmPAHs6F6opFnIlp2a/2UR/c933uL67YwO/Jc1m/V/TQjBTTCqFYUAPrdogd7juiNFlSJzENBKRPe3teix+e3u3tkCkm3BIgFEgM9ogI+n+bx9usftCnz+9Em3JdiuZ76imz8KAazUByWvDSLKHoCA9QsdjdqVtNiPdzbpRhH3HkPbp7sbHAFgOOyUjNMADrUvcVoC8QEpAKbPXkI76PYaAEbD+SIKAeiN8/Tv7r5b/+Pqjaor1ugXRVwXwo37l7xR77H5XgNgkpLU1KsU/bbh5EFZ3UhCwW8JxvCiswME+wGErT/3UTgiQcxoGfjxyR7VX76n75w8qW/1n9Mdh5/TTavW6xPtt+gnJO/AD7gA+2fn1DvAAPIvNNXqw8YuRdHfnF3WDfYs4u4PLVjsVP98yQ8ltmS90Y6JQU91X+dIhcpHbf/pPR/RP09Uf1r+/wuNYP3mhAAKzg6AVX/r3IVuFMCdF1BuUMmXVHLBkGMyRwDg+0NFRh8CjAQQwT+jwQ9ejQD++vgp/Yv+QX3q2QO6+c67dX/HrfrxxGBHJUEA/6rVt+K0rNu6uoYJICv66cXtFQJgzB/D4Z4FLMsVzTPnnxY6P8up7Bm6DQ1dLk2MdhjvdMMW/T8TlR+bAMbAv7/zI94GUFP04/50P+Zf57oAjWxOkmd/AqYF1+iNInpLMnTozyuwMwsiAcx4IQ8aplgXKdJ/51SP6nvvKQTwTn+/Hvrjo7r+njt0izTqF+be6Cbt0OL//o3tzthnFfiFhYtcCz4nI06lf2xJZ4UAUPXX5USfuHGuLnIGO7oRTOttUKltcyMIn2uYrfcnH4ZhwP9+/8f134roPBFn+f8jEf2Pm+72GgBTgZPRhG2dC3S90xpKDvwiHZqXsj7SOU8f7ZrtbQC5gp9RyMElwSzAtPofNYCUMESgzLwu4flebwNgOfBf9Pfrzmf36IZPbXIVgeqP0e3JG25wxjmG7JiCiwZAi/uZWc36mdZWfbRjlj7dUauPLer0K/9Yiiui7dgG5jTo5xd563yJRUO1La5bsb+lQx8VUYyIH4VgRPStG5frz9bfpf+4+lb9z3fepH+ABpLMIVhfEP2UiB5rbnHE0eVmHTarZFq1KEX9g46FurVjvhtRsMlJ44E/EkAkAGvQZqzrCEDf0/OnT+mPBvt1z+G9uvqhDZqdW6fFnOhqZuqZal2T0wx97MQQiMrNZCGGAZmdBym4GYP17SqlsgMv8WmxMR5yVBdxMQI+ff0y3dbSor+9uNvFQxt4RET/g4h+ib6+iN4VtEiP3HCD7pkzT59u73LlaWdzUXYuzjS4RUOU4fbE2MjCpGqtfTW/Gfvhg7qNdTCDifCdU6dV33/fnw041K9HjhzSzZs3OKDSl29KRgHcZhm0/mzsiSbgWmZv3CMcar+z8jvBYjmwX7xD94EL0BPOWekz/h1W+6Jk3d4BDc4WUNBO4fLaA/G8cHJQaU5rJaezJKetUtBy5dBRf+aALRbK5LJu/YBfBZhMBBpjNmAUfqvj6M5IWfirngsJYEtCAFSIm2PvVt7l3fx7wJ/jmYk2pbJbkCNlJuXYYh4PdADph/384aGVyqU/D4Gw6g8LvususOqvQcXt5DNbJcuaf/rvJpTsKwjQ61TY60/KbkmyIxSmJ7P81y0xpouSHE5iW4KbO8pQYKVcFbKxPKMb62YGyMBbpz0B0AU4f7ZfDx07pOsf8BoAApBnCi5XpqhZtz9/shTXzb1ni+9k6i1r8ZPVgMRDA3BagguXgB5AozlwQQJcCcghC7QEVhTS2rtThpIuhQf68MfgmfRdHuTjyCKvgvEv69V/uiJcDAeONRcgCvlwvca6mIF1cb7X7wdgNoCDzx3StQ8OEwDr7/1Ze0XNZsoebLbmH00A8Lm+Pf17vxwYQXKgBdymLbiwQQVDApUW3oOf1YBoDp4I2NyTywOZ9MKrQgCc/Yfan8lXdgEG8ITFWGkkUK3/HxoB7d7cywEGK8OlSDvc0uxSpBfTCGRzJmmDg/29ym+wl+PBB93x4PdtuS/pe1dvQR1wAW+lBccW4O0B3jaQVKaBnLB2mQZgblLZBmgW9nCx65C/RgIfQUUj+cGrL/kyAnbKIeKO9nrllVf09dd/4J4dCSXpf/s739JvPP//6iuvfr/y30KhB1CcDuRsHaN0FwzAY7m1tbVuk1HSsvQtPBuRTjZ90rByWXrmh/v9739fOeHoxRdfdOEsr4m6YZrxfgaSQP+AJ4C+vjN67tygHjlyWDdvHiYAN5fe+tFV3AkLjQEedwTDGnkwmy+8zH9k+Nq6sn73e98eTgMVH+3CEcB3h/1R//MZpwmUCnl97QevuI1ELe8iG5mOKIffimyyAA2BRtwwTXvm0BH8w7ATvbcdiwlPGpCIpRfm9d3vftcRz0TTtXBhGvF+pKzNiPq4YgSQAttw5RrQzTUSsOcLP8pLL3mgQ06kA9Bx8S9gXEzlBdghANMUQvADKFpRi2PAmKpLOrTIHDQanjVgJw/xfjJpW3jS+853vqMcZmplRdswkuG9hZ1s+pZedC+UtWlfJ5MlACdkgSYw0Qoy8F0Y3oBu7oUEgEBbvJdffqkCeAO7uRCAkYKFt3fES5eB7gCgMvAA0smAp1pY0iNvK/O3vz2srVQLP54fab3wwguVswt5Jg+6BZCX/U/7D+Oll35v8aM7A8FPQ5kmgL37duumTRsrQAJABqoyc/IR7ixn6RWUljQNKhMkwtAyI3D4Iaxc2Wze7eBTLJTdPdb+cplzBAlT1GKhVgt5TvdFuCEFqbRy3L/62svOz/knG35Yi/7973/PlYl3VmaL//LLL1cFN0Ay8BA2faUBM97zN77xjcpBI6RlB5AauUwl/VdffbVSLlp801goS6gBWF2HeYxX3jBsvL/w+0/7OkkTwJe+/JyuXXuPAzgg/+EPX3OqNcADVAAevxMnXq8Y1L71rT/XF1/8pgM8LS1hrc+NUc7O4KscyvmD4/qd73xPX3zxO1pbywrDrL7wwjf1lVde0++/9JobTXj55VddmIqwJ+r+RAkgJCZAYgTAfXhdSgKA4AB6uVyuEB8qewjUtEBNBqAQgaWXTsc0j7T/ZNJPx43PM4AQ0gRw8OD+ihEQYCME1sICPoDFc319rT7/wp85i3sINhMa1GsuAGF+uK+95s/gQwOg5X/9h75Py/OrrybW+2zevTt9+nSl1bZyYOG31p1yoKHU1JZcuSif3VuZATvEQ0ts1vTLRQCAjXKaa6DkmTzDerD7iQDU0rM4EEE6PYyA9j50J5J+GD7ezwDQh5pumgC2bdvqugAmCIAN1fqFP/+Ga9XNH9es8WaEw8+Ah4bAM6Czln84bsa19idO9OhL30M1H+7LGgmcPHmyAiTikQcXGsZwOv5jWf6Ux+7TYUyTSPtfSg0gBGoI/rCvns4/jMO7NGDT4QE+dZP2H60bQ3pGFum003mn04zPM4AM0gSwfceT7mgw+/jHj/sWm+4ARAAhGMhR8y0crhncELhQII0ATBABY2Mj23mJ6x4AQu4RSLoM3NOiWTyeTcugDDyHfpYvRkADm8XFUk5Y8jQbBHYIm2nIO6z2Fs/KiBpPGtVAM5Yf6YWWelfOpPUnbf7rZIEX2gBI75vf/Kb7T5TZ6o4uDu/SF8OI9p+s3Okw8fnCepsxdZImgKNHn60QAF0AAxfAty4BrSyAPNlz/IIW14AEqKhEe7YKhRjMIMY7A7y95x0Cb8A1/9BFC7By4W9dAib7GLhM6N37TGYEIeGHwRGXcGao45kL4GO3oKwGmom6PT09Lo7lb5oA6XIfgjldN5Z/2g1HEnhHnZE+4AfglC39HywcQ5FWFiPFdPrxORKA2kSgr33tq7rmnrsdqKzVp29N60rry0XfHhCictMnDw1zCCuCTguOsAMka6UQQISeMLRYAIwwvb29I1ou6z6MJphhNwBthMlBkFKokZAnrTj5AZCwC1BgEZKI/vAHx13rj62B8lImAxblxm+iwLdwzMgjHUBKnmkCwJ+w5N/U1DTif4/2fwlPOsQNidWATTzySgOc8BCDEU1LCzsozWBhj//9wu+f1gCeOXxQ169fWwloLS1kYMID2DAC4ofRzfxxTSgBH60TQOQyfwtrIOAZweU9LqMJFmY0F+2DcICfsjA8iRYAMUEqXBbXQAGYPTj9kBrdACOCcEKNxaN8qNq4E734D/xXwuMCvPT/pgzkQRjLayw3Hc7+j+UDwLkgiHRY0jUCSpdjrDzjuxlEktUIgOPBJysEpoZfGC/rjHw2ru8366BV9peFp2VDG0CNNz9c0h3rggxGXFnyC0E7nJfliWvzEUI/7smTlpMrLIfdj0w7zGfY2GZhQxdVnDQNiNXIgfDp9MM0qr0Pw4dhrT7Nj3B2H90ZBPDxtJ5qBLBh47pLKCw2w8+7IeAAoQFiNKEcC/xV340APwCtTgCj+Y9WDvMPAVft3sLh2vvQj3v+s13pdxbH3PHeWzjc0dJMpxGfIwFUZODDJACzxCO8FIhWEZWeC3DjVxXkY2kFF0EANvOwUjlV2DMEXLX7seK6/5d0Cwys1dII/dLphe/S9xYWf+7Jz+7tXXQj+EfIwNVAAFagtLA2NtZfNgKAfNAC0l0BK8tobhp06efR4pm/Ad/cdPz0s8UzN/0+fLYwU3FJZyrxYpxrnFAGBvvcfgAQwdDQWT387KHKMOC18HFDAFS7t/+AMez55593IxDmZ0ZKe54ICKrlEfqRlqWDoc6ezS8MO5F74pMOhMF96DY0NDiDJ0ZADJb2jpafsN/61rfc/8W2gvHQ/MnXbBwWBzdqDNc4mKtorMjBmNd0JwCEnbkFNh5uoKNSAJaB1IbXxqysoF9v6aRd4pMfF/cAixER7uvr6yt2gXS80Z4hKeLyHje8t3TxY5SjWljehcZHiw8h4G+kQDmtDISJ1wypg+lOAAiyEYAJeyjcRgCjzaQLw3JvIBnNRdOAbMzqz+pAwgKwEGSjxU/7W54MbZK2XeZv2oHNYcCf/2utOS5lMbKgDIThomy4Vi9GIPY+ujOABKY7Adi4edjaGRhs/J936VZyNOFPAzT9TDcDkAEqA5a5pJkOP94zcdL7AaDS48//4P+Rn5XfCI08ucflHeGtLvCj+4AfhEIZuI/XDKyD6U4ACDUAoYU0QefZWjvARZjRNIDxAJp+b+AMwRQSQOjPfTp++jmcwUi5q8XHzwgg/Z7nMI30e/vf5Jt+F59nACHMNAKwvjmgBKy0klzp1Ycm/GlAjvcMELEnoLKHc/irgZc8xkvPVHvUeGYRUmYjL+KjBVB+8rT/ZmU3dyIEMFr5LI3oTlMymIkEAGAQ+DQBIOTjAXK899aiGqBYU2BxqoHI3o3mQkw2nx+wW7lJi/9h2sXFagBW3mpljH7TFPx0+2YaAZgw0zoj9IAI8PFs96OBcSL+AJK+trXMtNzkSetsICMdK0d4j186DyMU3tkSavxI38LjjtXKj/XO0reykVa8ZlAdTHcCMHUZEFhraaBDA6DlRF2npcW1dwB2KoTAeLwZ20jDCADAkj+u5TERoNna/zCsgRY/U/tDP/InD1ttyBLlMD5xjEwoH//T3hNvMpfFi+41ShrTnQAQTAQcoBsBGGh4h5+9t1aQZ/rUU1kOjFUdkFsLbfkCKkCKOs+9lWs84BgBGKkQPgQ7IxmkR7rpNC0fe8f78D9S1jB/3hFnMlcYP95fgyQw3QkAsANyWnsTfgQ1JAG0A4Bq3QLC03e3IbLJAgKAkh4EQl7ky0UZwnI0NzePAGA1ABEPAFsZR1Pn0V4ot2kapGVDfaNNcmLI0uoC0uMiv8n+32rljn7XCBlMdwJAmBFGpsUi8ACQZ/MfS1AZIpwMGKqlCaBCsrGRgWphRytLCGpASjj8aP0hGy7TFMI0IDDeQURoEBCEvcff0jF/0rzY/2vpRzcSQEXYLqcwTFZgxwtPWWm9uaqVe7z46feWBq2wkQ9+hLN3Y7lhetXC2XuIxlrvauHG87N0JuuOl258f5UTwUzQACYj1OMJ7GTSMlCOl+ZY78P8xgp3se/CfCZzf7H5xvgfMkFEAhg2ek1EGKcCDuKQNqq23U8kL8KE+U00zlTChflM5n4qecU4HzLow6HeSADDBDARcF5pcIT5XU7ghPlM5v5ylimmfQWI4longCgkV0BIwhYj3k/IdnPNyGUkgAiga0ZYI/lcevKJBBAJIBLADJaBSAAz+OPHFvXSt6jXWp1GAogEEDWAGSwDkQBm8Me/1lqrWN5Lr7FEAogEEDWAGSwDkQBm8MePLeqlb1GvtTqNBBAJIGoAM1gGIgHM4I9/rbVWsbyXXmO50gSQZX18/JCX/kPGOo11OhUZiAQQNYDYBZjBMnDZCSAjKnYlrX/UAGawwE2llYpxLp9282EQQG5S3QAOw7jwQIzYakUSiTJwCWRgmABO69AbAxd/OnDQ2rsPZM+4rIlProlpAVmVDFtg5S8ggUw2+fOWfqqViLaGSyAcqTqNgJuGdTo0cEpVf6WDAz069EafHn72wIjjwQ1IoXshsK2VzqoATAfOrGYNuAFIIQD3vk5UGkSlVlSK3o88hgmCNAF+jUo+q1IvKs2i0iQqheQiXcvP8shZWlnNCWWYhh8t/qfLpxLPtLp9u++Hqvoverb/hCOAnbu26YMf26zFjGhdYdhi31AEjB6gDlScU5cD8B6oWSl6wALAHOHKWpDa4dYbgFrl1ogu3jZfGx9r0OVPrVTJi0qdaF5E6ySTkAAbWJY0k2l06S3Zt1RLe7Pasr+g0iUqjYltIcnPEQHplDw5QD4FKWr2CnUf2HQz3Lqb/2p79E1mg43Jhq3UqdVtdIflLNbF+HXxTu9xVX1Xh/pO6PmhPn3uK4f0/l/b5CMCJlrYdlGZK5rpFM1mRAtUrGt9UdEhBsDPSTX54dbZgW8kAVRaY1rzz4rKIlFpSTSA60XlOp+Py2+2qMwTlXJepVU86G8UzX0xiEc5jABMG0CbKEBAWS1K/ooRQAhEgG/PkwX0ZMNbPtENGpgI/Ir8jSsXb/aeVX7nz/Tqm+f6dO8z23XNr9/lErjxD1fqnD3tWtqV1fLBOl26+zqVsmgD21Jz4IYz5hn4ix6MkEY5ATXgzCTdg4zXJlwXoEW080CzysKEXBaLym2i3b+4Tpe+t0Bv02V62wc3q9wiKt0JyNt82Kb9NSpzfFfAax3kX9Sca/FFcxBURrTIcdiTMjZenADR+rPrr+3bD5Dt0I7Jgnoy4cf9wBEMEwfDTKyrN3sHPAH0ntY3h87ol//Ns7piw02+5ae/PV9U9okH66xE9QbYqNu0tjUJ4Gn1uPAzAiBMYg9AY0ADaK2tce8bdxRUOhMbwGLRBT9fovI/icrDovJrovI7oit+eaPXEnIllWLZ2QC6drZ7jaSB9NAwar2NAHtCvWg2J1qbENRYBADILhV4QtWf8wdMA7BNQCcD6MmGvVT/IaZzcQ3ANVt/P+79vqr+Nx0aeFWHzp/So8f268b192gJNsTY1iHavmOWV9Xpdyf9daFFRjVHVYcEuOhvQwKu5adrwEU3ITEOciIP6RbRABq9ik/3YrHokg8WqnxCVFaJys2iskl0+X9d6AgoK2UtS7Mrz/wn5vl8AbzUeQKgHFuLmt9WciSAdsJ1OQgAgNrhHOFHx493HMJh5+6F79P34WEhaAq8twM6LKyRAc/cG7HYe7Mx2HN0ZyiIL0Zz+esz31PVn+jQwMs6dP6kHj12UO9bt1brAS5AbhOd//icBNS+lb3hydW64OlFKktEO3Y36YLHO71FHxKogN+r5o4E0gRQEu3a3+wJgDhzRT+qy1V+XVRuFJVbReUB0ZveXe7eYcyrhQCKonOfnOfK5EYEjAA6ROX3RXOPFp0xsShFB37fRRlbKDgCjFN1OH7LjvIaD0gAr7e314Xv6+tzJw4ZGC0NugMcOGppceoOJEEX4cSJE5WuAv4c0MnBIS+++KI7kCQ8kszi40cZ7UQf/Ilr76M79neO9TNK/bxz5qSq/lLP972u5984o88+d1BXb1rtW3Ra/Hmis59q89qAM/R5UpCnRGW3OBKgn+5IgCE9AI1h0BkHAy3AEcOwBuAIgL48w4Fdoqvfu0Xlt0Xlfq/+i4p26w2OAIpmyW8S7Xi61RsEafWzNZopNqtw5BXdlRpGEgpadCMQwYjFKAxpJ+MCTFpfjgIbT1AIB8itBQf4BkreAXwAbulwFJgB9c/+7M8q/ry3M/t4Hx7gyTs7QoyyEQ7XuhrkwT1ageUT3VEEfJRvH+srqa83+86o6gc61NfjRgEqBACYGXefL9q6o80Nr/k+d70jg8IzNd5qTxegQ7RzT6LSo5obARgJYKFP7AEFyTktYe7eDm8DgDAWiMqdogt1jq7QW3WBXq/ye6Ktv1zgjIBu9ID4s0Rb97T6eIweSI3mio2axz6QFc1nUP2LWpbaMecAACYEACDh8mx+ExUMWmQDaQjENJB5NrKwtInLYZ6nT5+uABjygUwsjJWNZ7QUSAbCgny4h2y4LHx0IwFMSQbeGEAD+JUO9vuZgPv379Z1a1dre3OLn6QzW3T2rm4Hvsa6Ft+vrxedfXiRt9BDEnWiS/fP8iq965vTMpWSC21geFSguTzLkUHnk50uTVdojIErk/7/UlH5qKh8XHSJLlVheLCUUSnlXPi23d3eCFimta/VXK7oiQrC4mL+gjS6eQgVG0SqFTCwh2CdbItKGsQBjJzCa60zILVTeQEo4OU/Ep5ntIOamhrnF54/aKMHhIUIKJsRS0gG+BmhhIQxpY+fqpeYxgwkEdMAzvb16vlzZ/WPvvYlvW/LBm+9p3VuE+3c2+1bXQx29LdnizY+2e7vGctvE23ZmnQN6DY4wSppVrgSAyAGRVpxyTjAzj+w0BNGMsPv/p/+K5Xbk7kAy0U/+dOHPCksSYyRySzA9qe7K3MHSs7I6I2Rc3Y366JdnU47qZVZyQhBYoQcRdBNBTfBB3TWqtLSYtG3d6FrwDXQG3iJS+tOWO4BqtkEAOuZM2cq6RHXwhLe0jDQWzzeWTh7Rzkj+E3OohvK5qTv3+n5EQqAvt1zTt8aHNLdz+zRNb+x0Qnq9Y/dru17OrRlX4PO+sMWXbJ9setr33T0Bq3bWdL6J4vO+LfqmRVau1109o5a3xo7VbygZSn4qbj0/wE/LmCkv/6Y+NadyT7XiS7/yRpt1WXarYt0zT/d6d8xTwCNguFHVP5u0Tl0ASCZ2uFZirynnF17ul1XJSdtfmISxke0jxQBGJDwp3UFUFw8j0cAgJo4tPwQASRhLTIgBqwGXroIvDfCIH3u7YKALF/iWlmID8C5KCsu6fIew2JY/vR/i88Xfu9YJ2PUyd8eP48NUN85OahvDw7pkT9+Tld8bLXXAAAfw32AlBYYox3PuBjhACJGPMAJSAlPiy6MxWe0XnLBrEGbE+DDde9eorVP1ulN22/26dMF2CIqnxSVO3yeDYWM1kEaWdG7di7X+Y+36PJti7xBMlH3MxALhGJXEWJoTmYnDvep00JgLShgMiPdWMDiHZep/qRHGkYYYfrmx3uG+Ezlt64HYZubKaNPAxcCIP2wXNyHZQrfo0GE78L84/0YAp9qDGZ8Xf3d8eOqv/ylvn26R988N6AHjxzWjQ8+pIKxjsoCaIDawA3g8aN7YBN+mP0HGRAm763vjMMzIafWzdBLugFOA8BgV/Zz9i0N0qdrMTeZeERXo+RbeNYkuFacvCxv7gG+GRdtQlISp+AWAQUjEFU++lTAM9U4xOMC0OmLOkabMI3CBDINfvMP3amUJ4wf7yNRyP/X80PVX72r591agAF95tkjev+Wj2tWCpqRnJakrIyr52ntJONUeqzygIzx+ZzU+8k4uUzSx/fA9WGwyufdnHwHVjcrkPkBxKGf3qw5lwZxkinDZjNIugykY5dPo1YlW+fWJODvZhpmPekw7s9UY+fv7ANj2wCuBADGAr8BGLCH2gHlmggBXInyxzymOUm80eenAp/tO+2MgBDApgce9MAS0RrXimc1nymqZLDs+xV2vnX3gAOYbn2+9fUBL1fWg9Evy01aZFYQsry3kFfJsVjHEwQLdyoTd0gnWdRTseSTHn7FokqBVYJ+1aDfLMRa+2T+AcNprv+f2ACq2AGulGCPRQCAvL4eMvSAN6Mi/lxXqowxn2kO8ioacOWbn+33i4H6B3p1aOisHj58RDc9eH+lNQfo9cIYe1ElW1LJ0oLntSxZp+Lb+n4W4XA5Q5+BFSA78KE9eLC7JcTOSCjaKFxZrZO8G7d3YS1uEZIgr7IbTSC/ukq3AuKhi+LTrOw7gIZBnrgh6MP7sSrjMrwbjwAM/Lg2JTi2/jMYkJdBBitgr5b2271+HkD/QI+efeOsbt/+tK5bt67S+rTVAMLkg+RzKsWcSh7Vv0GLUuPW8OeYhANJJOFKOdEahv14TsDnN/rwrRpAfmr+9frM/Bv1t+au0IX5WT4s4CcONgbi09pLrdZJSb+weIPunr1Kd3Zcpx9JSElyGS0Kow0ZzZjWgD0i7zUX8qFMBkLcyn9JymoGO1z64en3FwtGGyEIVfywHHbPxCCMhZafxUuXJz5HcrikMvCjfjYEeVf7zp7QwfNn9djRr+oDG7a4vjQAWiCiLQG4pVhQybN4pUUz0qCZjJ/ZRxeAq5ATbSjktFUybkGO648nKwEpeKbUqJ2S0QO1nbpLyrpSRJeU6p02gLaxiGcRnSOiTdgaMn5Pgftknn5KivqVhm59ACs6AM5DADmXjxsNAPx0EyZBACEArWINhOlnC2v+E3UZZTBAc2+kk44PCZgf3YHRwlmY6EYyuGgZ6B/yOwKdGnpd+98c0K986U/0odWbtFNEV4voZxrqdVv3Il3oAIkdoEkl16qSbXBz8SVf8FpBIaNSzqnU1GpNpkaXAeoMiQAAC0JJREFUSq2uzDSrm8ePSm7qealWW6SgT9S3668lrfAsEd0toj+9fan+7KPL9Ce3L9P/umaFPsLyYRcGTSDjuhz72jwB0H1wMwQzrMLLJRoD4C+oZAuOjOiSOGJKrPBjAZixd1PBLVxPT49bKMT4+1QrmpYf8NtQI/kwN8DSJC97x1g/WoCRBUQ01XxjvEgOE5KBU+d/qL/Sf9GehAAO7n9O77/lXtcyf6alQx8ScS3ub3XM15UCeOu0Rhq0nLS8tvEG8/C5yBTNYb3U6qfbl+n85NkRAK1zsu3XtrY5Ll1abGwMP1u9Ul8W0f8gov9GRF8Q0f+y6V7tAOi1da5Vz4jo9s5ufVBE2/DPZ1QydEey7hm/nBRU2D+A7kRuYgQAGA1s5gJ+u6fMTOk1I92EKtYR10gh/PrXvz4C0EwbJi1IgIsW3yYRTTWPGG9kncf6GKc+zrxxXD/Qd/XMudd18PyAPnP4y/rJVZt0a/cK3Syo8kVtk4KuE9Gtszr1bhHXB18hoktF9CYRRxa4aAnLRfQuyegnRHRHsVUflpzeLvV+QlA54yz4qPo75y3WTQlI6GL8/aqV+r8lan+7iH5ZRP/T6rs90Gvq3KgBIxJPdM53BEDXhKFIkYLrKjw3p1O/NL/TawxutMB3BdIagIHNXASE2XhpdTucvQcRAFbiTFagrO9P+qQRkootAMLPLsjI4kw2rxh+HGGvQsozvs4Gzvo9AQcHXnfbgh949sv6iVWb9Kl5EEBBC1LvjH2A9emmZl0lop9fcpM+MqfVkcL1Ivp7y+fpp7uzjhyWiejvzF2oexua9dmaWfpE3XX6u92rvIEQy36u5FT5HfMX60b3QfIO5H+3ZrUeTTbxYDjw34voP69dq7MJU2TXn7zTFJ6a7QkAW4FfJpxx9oC9rc16dG6bs1e4jUGZkJTYJQzs1VwEICQAA58B1YgBQjC/yQiNpRf26TE22joEA765kQAiiCcjXxcd1jYFfbP3dTcTcM/RL+uDd27Sp+beqg9Ixu3/R38bAvhC+yztEnFq+eOzWx2A2R8QS/unF5QcAaDOYz9AAzjUsUAhhGbJ6CzBYIctoEZLklEIYEvCyKTxdw88oP+7iB4T0a+JqM5q0H+57RadZwSQyztD4Y6O+foxEVcON9afLIklXy43DFjw3RHyc3aAwAaQJoE0ARjg8QeUhLf++lQIgHSsT28fix2DIATrehj4cSMBRAIwObki7l+fOu5mAv7Vqdf17cEB3f3cMb3/rvW6c84K/bhkkrF6cWD/bJefvw7QvtDYqA8nAKbF/c3OvG6wZxF3f2jhQqf6F8rMKhSdla13BEDL/eS8pZUuAOkdEtF/uPU2/fuND+m7996np0T0vVUrXLfCawB+3sGTHfP0frMBsBSYPQeYhWh5M3zIrsDYJJxNwPev08C3Z+KFGoAt5bWW23b1MWIgXiUvy3MCLumFNgTSw+ofgj8SQAT/VGTrouIYAfzNyRP6zmCfbj+6V7fcfYc+XtOtnxS/AzAZoAH8blteSxk/xv7k3AWulbfMf6e7WdckQGDoj6G6PQtaHQgLdd6a3Vhod9Z8hu4e7Viq99I6ZpluLPobjDgkE32wI/w/IvruPXe6YUhnBGxmm2/Rz3cucGSEbUIglEy9m014o4jeksR3cwhs+XF2fAKg1TVgY5E3oNpyYHuHPyA1q7399/FcIxOzKxCfdOgG4EI6lsfzzz9fMQxavDB9woVX+C7eRwKZtAz85Znjqu+/qxDAXw6e0Wf+7WHdsHaVU+e3Lri5ogE8cvNcZ/yzDLYuXuZIASs9k3weXTRb1yYEQB9+XU70iRvn6+JkHkGT1Gre7evX6mb+fb5prm5OxvMZ6nt98/2OADAkXieif/Gp39L9kvV9+lo/XRbD39b2Tr1PRNs5MYhDQzLNmpesPtLVoY/OafHhbTYhJIAdIAWa8Nn+j+3uY8+m9hMWP3vmHkt9+GxxxnPN6m/hbA8A0y6MIKoB3+KEZbey2bvoRgKYtAy82e+NgO+cQgM4o7uO7tINn1rvhJ7JNp9fcp1uv2mlswVwUhDDa7TEN9Nit7TpZ9tn62Ndnbqvq0kfXzLf7/qb8TveYM3/13Oa9dHF85yhr5xpUalvd8OEexra9PFkBAFj4E/uvEf1+ttUV92vf7Xpt/XWipXfGw3RQH5fRI/U1zjbQbsb7qtXyTEjUfQPOufo1tmznX0Cy7+zBVQZBqwGIFpk23SDFplK5BlAAnRbrWfv2NVnKgRAupAAm39yURZLkzKwOamB2rSNdHnTz5P+4BPorsQ0ZxCRvNnvNwV9s/eEvnXujO47ulvXfHytW95bUxK9J5kQ5HYJrqvRDCSQGPpQuQHvHSIOlLc50OZU6mY7yz3zAegWYBtgZl/R7ePvpxYzuWhPZ5f+/vJFLsx+Ef0/RPT/puvgDHos8Gl0W38zvr+tc4Hua2rR7a0tbiSijrUAzEjM1Tg7AzMKb0+0DTf0ZyMAE9QA+E9mmTcAADZaY0BqQLV3f/qnf+rqwZ7Hc0Ngh2HNH/Djb60/+TExKQ349HOYVryfQcC9VET+l6f94aBn+/3hoPsP7NING9e4OfxM7MFCD5Ddqrzk1B1O3vHC5sFMF4BWmItlvRkpaV4ybiUh8bnYH8At4GE9QZ53bBiSWOuzPgwaw1zJa3uyRJg8sA80S1ZnSVZbE7eO/j9nFXIxCpAbzt9NCU4mAVUmAo1DAgbCagBKAw6tIFTl03HD8NXSm6hfmM5Y9xNNL4YzmY3uCFn48akLCeC+jWvcmnq3ug+ws7TWnf/nj93KomKznLdU76b+CguGGON3i3myFfBDCJIFpFjrk4VBLNohHCv9SkW/sQiLf2q5r1cptqnk/IGgxPcERP5sJFKrwtqAfI2fBpz08V16NvknWQswAvwTIAAD2YjKCWbp8T79rppmYOlUC5+OP9ZzmM5Y92OlEd9FsI8rA2/3egJ48ww7AvXp7oO79J7NXgNAlcaiT6vO6Tz+ANBkXn+eg0DLKgUAySYdvMcyn3Nqq1uFB1EYMK1Vxo+LZ97ZrkD4iT/S25YYE872HXAEYnFDF0IxUknuKbebmpzMAxhvLkAIsHSFhe8AvBnswnBhmPA+DDPZ+zCdse4nm24MH0lhhAy82TdMAG+d69OnD+3SNVvWeOt5stOO39DDCMDG3pONPVzrHrzL5lxcpz0ASFppVunh8mwrA40EkneAHrDT3aC74EgiO6zacyqxiw8psfeAI6bhcC58svjH5gCgQbi5APiPMRIQvhtROSkNgHDp9zyH8cP7amEn6hemM9b9RNOL4SLwq8rA2QF/MIjbEWhoQPce2K3r77vXCfqwBuBbZ7/7TqLKA0hriSvbeSXvQgOFhTHXugIWH1Ko7Bzkge00gCSc10CCPPE38Fs+zo9ugrfg23uLi1v1z0f/WC8zXQYGBj0B9A8MHwyyYeMwAVz9wDHgV3OtCxMJ4Or/jvEbfSjfaPoRgO0POKwNfCgVO9Nblvj/rw3tanoTQCSBSH5RsxhTBgYG+5SfbQq6f/9e3bDR7wmIDWDMyFcFy6dV/1ADiARw9X+/a0HGpnEZIwFM4497VRB0rN+rmoSvfQIIBSytDUQN4KoWvkhQH76GPb0IADJIk0BIEPE+EkKUgREycOkJwAA41Yq+1PHT6dmzuVMtZ4w3QpBia/7ht+ZT+QaRACKQI5BnsAxMPwJIf8x0S2/P5qbDx+dICDNIBi4tARiozJ1sRVo8cycbv1r4dFr2bG61ONEvksAMkYGLJwADkrmTHYe3eOZONv54H8rSnag7XnrxfSSHaSQDkQDSxDCNPu5UjEIxzrVpzJvid/v/AddUkwnpH4dbAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [1, 2]])"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vstack([v] * A.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3],\n",
       "       [3, 5]])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vstack([v] * A.shape[0]) + A"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "np.hstack:按水平方向（列顺序）堆叠数组构成一个新的数组\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [1, 2]])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tile(v, (2, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3],\n",
       "       [3, 5]])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tile(v, (2, 1)) + A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 1, 2],\n",
       "       [1, 2, 1, 2]])"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tile(v, (2, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 乘法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 2],\n",
       "       [2, 6]])"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v * A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 7])"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.dot(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 8])"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dot(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 矩阵的逆"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1）np.linalg.inv()：矩阵求逆\n",
    "（2）np.linalg.det()：矩阵求行列式（标量）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.5,  0.5],\n",
       "       [ 1. ,  0. ]])"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.inv(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "invA = np.linalg.inv(A)#转置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.],\n",
       "       [ 0.,  1.]])"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dot(invA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.],\n",
       "       [ 0.,  1.]])"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "invA.dot(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.arange(16).reshape((2, 8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "LinAlgError",
     "evalue": "Last 2 dimensions of the array must be square",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-207-60b1a25f4891>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0minvX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Users/yuanzhang/anaconda/lib/python3.6/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36minv\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m    515\u001b[0m     \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwrap\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_makearray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    516\u001b[0m     \u001b[0m_assertRankAtLeast2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 517\u001b[0;31m     \u001b[0m_assertNdSquareness\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    518\u001b[0m     \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult_t\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_commonType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    519\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/yuanzhang/anaconda/lib/python3.6/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36m_assertNdSquareness\u001b[0;34m(*arrays)\u001b[0m\n\u001b[1;32m    210\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0ma\u001b[0m \u001b[0;32min\u001b[0m \u001b[0marrays\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    211\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 212\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Last 2 dimensions of the array must be square'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    213\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    214\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_assertFinite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0marrays\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mLinAlgError\u001b[0m: Last 2 dimensions of the array must be square"
     ]
    }
   ],
   "source": [
    "invX = np.linalg.inv(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 矩阵的伪逆"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -1.35416667e-01,   5.20833333e-02],\n",
       "       [ -1.01190476e-01,   4.16666667e-02],\n",
       "       [ -6.69642857e-02,   3.12500000e-02],\n",
       "       [ -3.27380952e-02,   2.08333333e-02],\n",
       "       [  1.48809524e-03,   1.04166667e-02],\n",
       "       [  3.57142857e-02,   8.67361738e-18],\n",
       "       [  6.99404762e-02,  -1.04166667e-02],\n",
       "       [  1.04166667e-01,  -2.08333333e-02]])"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pinvX = np.linalg.pinv(X)\n",
    "pinvX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.00000000e+00,  -9.71445147e-17],\n",
       "       [ -1.33226763e-15,   1.00000000e+00]])"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.dot(pinvX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "矩阵的伪逆又被称为“广义逆矩阵”，有兴趣的同学可以翻看线性教材课本查看更多额广义逆矩阵相关的性质。中文wiki链接: [https://zh.wikipedia.org/wiki/%E5%B9%BF%E4%B9%89%E9%80%86%E9%98%B5](https://zh.wikipedia.org/wiki/%E5%B9%BF%E4%B9%89%E9%80%86%E9%98%B5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
